CHARACTERIZATION AND MODELING OF TWO-PHASE HEAT

ABSTRACT

Title of Document: CHARACTERIZATION AND MODELING OF

TWO-PHASE HEAT TRANSFER IN CHIP-

SCALE NON-UNIFORMLY HEATED

MICROGAP CHANNELS

Ihab A. Ali, Doctor of Philosophy, 2010

Directed By: Professor Avram Bar-Cohen

Department of Mechanical Engineering

A chip-scale, non-uniformly heated microgap channel, 100 micron to 500

micron in height with dielectric fluid HFE-7100 providing direct single- and two-phase

liquid cooling for a thermal test chip with localized heat flux reaching 100 W/cm2, is

experimentally characterized and numerically modeled. Single-phase heat transfer and

hydraulic characterization is performed to establish the single-phase baseline

performance of the microgap channel and to validate the mesh-intensive CFD

numerical model developed for the test channel. Convective heat transfer coefficients

for HFE-7100 flowing in a 100-micron microgap channel reached 9 kW/m2K at 6.5

m/s fluid velocity. Despite the highly non-uniform boundary conditions imposed on

the microgap channel, CFD model simulation gave excellent agreement with the

experimental data (to within 5%), while the discrepancy with the predictions of the

classical, “ideal” channel correlations in the literature reached 20%.

A detailed investigation of two-phase heat transfer in non-ideal micro gap

channels, with developing flow and significant non-uniformities in heat generation,

was performed.

Significant temperature non-uniformities were observed with non-uniform heating,

where the wall temperature gradient exceeded 30°C with a heat flux gradient of 3-30

W/cm2, for the quadrant-die heating pattern compared to a 20°C gradient and 7-14

W/cm2 heat flux gradient for the uniform heating pattern, at 25W heat and 1500

kg/m2s mass flux.

Using an inverse computation technique for determining the heat flow into the wetted

microgap channel, average wall heat transfer coefficients were found to vary in a

complex fashion with channel height, flow rate, heat flux, and heating pattern and to

typically display an inverse parabolic segment of a previously observed M-shaped

variation with quality, for two-phase thermal transport. Examination of heat transfer

coefficients sorted by flow regimes yielded an overall agreement of 31% between

predictions of the Chen correlation and the 24 data points classified as being in

Annular flow, using a recently proposed Intermittent/Annular transition criterion. A

semi-numerical first-order technique, using the Chen correlation, was found to yield

acceptable prediction accuracy (17%) for the wall temperature distribution and hot

spots in non-uniformly heated “real world” microgap channels cooled by two-phase

flow.

Heat transfer coefficients in the 100-micron channel were found to reach an

Annular flow peak of ~8 kW/m2K at G=1500 kg/m

2s and vapor quality of x=10%. In a

500-micron channel, the Annular heat transfer coefficient was found to reach 9

kW/m2K at 270 kg/m

2s mass flux and 14% vapor quality level. The peak two-phase

HFE-7100 heat transfer coefficient values were nearly 2.5-4 times higher (at similar

mass fluxes) than the single-phase HFE-7100 values and sometimes exceeded the

cooling capability associated with water under forced convection. An alternative

classification of heat transfer coefficients, based on the variable slope of the observed

heat transfer coefficient curve), was found to yield good agreement with the Chen

correlation predictions in the pseudo-annular flow regime (22%) but to fall to 38%

when compared to the Shah correlation for data in the pseudo-intermittent flow regime.

CHARACTERIZATION AND MODELING OF TWO-PHASE HEAT TRANSFER

IN CHIP-SCALE NON-UNIFORMLY HEATED MICROGAP CHANNELS

by

Ihab A. Ali

Dissertation submitted to the Faculty of the Graduate School of the

University of Maryland, College Park, in partial fulfillment

Of the requirements for the degree of

Doctor of Philosophy

2010

Advisory Committee:

Professor Avram Bar-Cohen, Chair

Professor Marino DiMarzo

Professor Patrick McCluskey

Professor Peter Sandborn

Professor Bao Yang

Professor Gary Pertmer

© Copyright by

Ihab A. Ali

2010

ii

Dedication

To my sister Rola

Your Soul will inspire us and be in our hearts forever.

iii

Acknowledgements

Thank you my advisor Professor Avram Bar-Cohen for your advice, wisdom and

support throughout the years of this work. I would like to thank my committee

members, Professor Marino DiMarzo, Professor Patrick McCluskey, Professor Peter

Sandborn, Professor Bao Yang and Professor Gary Pertmer, for their great comments,

support and advice.

Many thanks to my friends Emil Rahim, Vinh Nguyen, Henry Lam, William Maltz,

Ceferino Sanchez, Dr. Attila Aranyosi, Juan Cruz, Dr. Himanshu Pokharna, Dr. Rajiv

Mongia, Dr. Jay Nigen and Bernie Rihn.

I have great gratitude to the Advanced Cooling Technologies’ (ACT) Dr. Jon Zuo, Mr.

Richard Bonner, Mr. John Hartenstine and especially my dear friend Mr. Scott Garner

for their great efforts and support with the design of the apparatus used in this

research.

Special thanks to Mr. Phil Tuma of 3M for his technical support and donation of the

HFE-7100 fluid used in this work.

Thanks to my late sister Rola, your soul inspired and enriched me to stay in course

until the end. Thanks to my mother Sabiha, my father Abdulkarim, my sisters Heba

and Reem, my brother Hossam and my nephews Hasan and Hany. I love you.

Thank you my wife Alia and my son Sammy for your support and love. I am sorry for

not been able to spend enough time with you the past few years. You are my life.

iv

Table of Contents

Dedication………………………………………………………………………...…….v

Acknowledgements ………………………………………………………………......vi

Table of Contents…………………………………………...…………………...........vii

List of Tables………………………………………………………………..................xi

List of Figures…………………….…………………………………………..............xiv

1. Trends and Cooling Requirements in the Electronic Industry………………...…….1

2. Liquid Cooling of Electronic Modules – Literature Review……………………….10

2.1 Introduction………………...………………………………………..........10

2.2 Microchannel Coolers………………………………..…………......…….11

2.3 Pool Boiling................................................................................................14

2.4 Liquid Immersion Cooling…………………………………………….....16

2.5 Liquid Immersion Modules........................................................................18

2.6 Flow Boiling...............................................................................................20

3. Theoretical Background............................................................................................23

3.1 Single Phase Thermofluid Characteristics in Miniature Channels.............23

3.1.1 Pressure drop correlations…………………………………...….23

3.2.2 Heat transfer correlations……………………………………….25

3.3.3 Effect of heating non-uniformity……………………………….27

3.2 Two-Phase Thermofluid Characteristics in Miniature Channels…..……..28

3.2.1 Introduction………………………………………………...…...28

v

3.2.2 Two-phase flow regime modeling………………………………31

3.2.3 Characteristics of two-phase heat transfer in micro channels…..34

3.2.4 Heat transfer correlations…………………………..………...…35

3.2.5 Unresolved issues in two-phase behavior in microgaps………...41

4. Experimental Apparatus ………………………………………………………….43

4.1 Overall Description……………………………………………………….43

4.2 Calibration of Flow Meter ……………………………………………….45

4.3 Chip Thermal Test Vehicle…………………………...…………………..46

4.4 The Microgap Test Channel… …………………………………………..52

4.5 Chip TTV - Sensor Calibration Procedure………………………………..53

4.6 Fluid Selection and HFE-7100 Novec Properties…………………………54

5. CFD Model and Simulation…………………………………...……………………59

5.1 Introduction……………………………………………………………….59

5.2 Equations Solved and Methodology………………………………………59

5.3 Model Description and Conjugate Heat Transfer………….……………...61

6. Single-Phase Data and Discussion……………………..…………………………..67

6.1 Basic Relations…………………………..………………………………..67

6.2 Error Analysis……………………………………………………………..68

6.3 Single Phase Results………………………………………………………70

6.3.1 Comparison of experimental, CFD and theoretical correlation....70

6.3.2 Raw temperature data and comparison to CFD………………....76

6.3.3 Conjugate effects and conduction spreading in advanced

vi

microprocessors……………………………………………………….82

6.3.4 Temperature distribution – Uniform heating….………………...89

6.3.5 Temperature Distribution - Half-die and quadrant-die heating…93

6.3.6 Inversely determined heat transfer coefficients………………....95

6.4 Overall Single-Phase Hydraulic and Thermal Performance…….………...98

6.5 Conclusions……………………………………………………………...102

7. Two-Phase Heat Transfer Experimental Data and Discussion……………………106

7.1 Introduction and Basic Relations………………..…………………….…106

7.2 Taitel-Dukler Flow Regime Map………………………………………..111

7.3 Heat Transfer Characteristics…………………………….……………...125

7.4 Heat transfer Characteristics with Non-Uniform Heating……………….131

8. Heat Transfer Correlations……………………………………………………..…136

8.1 Introduction……………………………………………………………...136

8.2 Heat Transfer Correlation Based on Two-Phase Reynolds Number……137

8.3 Flow Regime Sorting Based on TD Transition Line……………………138

8.4 Flow Regime Sorting Based on Characteristic Curve…………………...142

8.5 Inverse Calculations of Spatial Heat Transfer Coefficient………………147

8.6 Inverse Calculations of Spatial Chen-Based Heat Transfer Coefficient...152

8.7 Prediction of Wall Temperature Distribution and Hot spots of Non-uniform

Heating………………………………………………………………..……..155

8.8 Conclusions…………………………………………………………..….158

9. Conclusion and Future Work………………….………………………………….164

vii

9.1 Conclusion……………………………………………………………….164

9.2 Future Work…..…………………………………………………………171

10. Bibliography………………………………….……………………………….....174

viii

List of Tables

Table 1: HFE-7100 Environmental Properties [52]. ...................................................55

Table 2: HFE-7100 Toxicity Properties [52]. .............................................................56

Table 3: Characteristics of 3M’s Fluorinert and Novec Fluids [52]. ...........................57

Table 4: HFE-7100 Thermo-Physical Properties Compared to Other Coolants...........58

Table 5: Sensor Temperatures for the Uniformly Heated 100-micron Microgap

Channel with the Flow of HFE-7100, Tin=23°C, q!=7W/cm2. ..........................77

Table 6: Sensor Temperatures for the Half-Die Heated 100-micron Microgap Channel

with the Flow of HFE-7100, Tin=23°C, q!=7W/cm2. ........................................78

Table 7: Sensor Temperatures for the Quadrant-Die Heated 100-micron Microgap

Channel with the Flow of HFE-7100, Tin=23°C, q!=7W/cm2. ..........................78

Table 8: Sensor Temperatures vs. Flow Rates and Junction vs. Surface (Wall)

Temperatures for 100-micron Channel and Uniform Heating with the flow of

HFE-7100, Tin=23°C, q!=7W/cm2....................................................................81


Temperatures for 100-micron Channel and Half-Die Heating with the flow of

HFE-7100, Tin=23°C, q!=7W/cm2....................................................................81


Temperatures for 100-micron Channel and Quadrant-Die Heating with the flow

of HFE-7100, Tin=23°C, q!=7W/cm2. ..............................................................82

ix

Table 11: Average error (

!

"AVE ) of Heat transfer Coefficient Predictions Sorted by

Annular and Intermittent Flow Regimes per Classical T&D Line and

!

We1/ 2

Bo1/ 4

= 6.2

Based Line-Uniformly-Heated Channel. ..........................................................139

Table 12: Parameters of Two-Phase Heat Transfer Chen Correlation on 100-micron

Channel, Showing Error Reduction by Setting Convective Enhancement Term

F=1..................................................................................................................141

Table 13: Average Error (

!

"AVE ) of Heat Transfer Coefficient Predictions Using Chen

and Shah Correlations for Uniformly Heated Channels. ...................................143


!

"AVE ) of Heat Transfer Coefficient Predictions Sorted by

Pseudo Annular and Pseudo Intermittent Flow regimes Graphically per (h vs. x)

Characteristic Curve, for Uniformly Heated Channels......................................144


!


and Shah Correlations for Half-Die Heated Channels.......................................144


!



Characteristic Curve, for Half-Die Heated Channels. .......................................145


!


and Shah Correlations for Quadrant Heated Channels. .....................................145


!



Characteristic Curve, for Quadrant Heated Channels........................................146

x

Table 19: Experimental (Two-Phase Test) and Iteratively Adjusted CFD Wall

Temperatures for Three Heating Patterns. 100 micron Channel, 25W, G= 1500

kg/m2s.............................................................................................................149

Table 20: Temperature Errors of Conduction-Only Model with Prescribed Chen-Based

Average h on Wall, 100-micron Channel Flowing HFE-7100, P=25W, G= 1500

kg/m2s.............................................................................................................158

xi

List of Figures

Figure 1: iNEMI’s Server Chip power and Heat Flux Trends [1]. ................................1

Figure 2: ITRS Power Trend for High Performance and Cost Performance Electronic

Chips [2]..............................................................................................................2

Figure 3: Trends in Chip Package Thermal Resistance [3]. ..........................................3

Figure 4: Power Non-Uniformity of Intel’s Itanium Processor [4]................................4

Figure 5: Power Map (Non-Uniformity) Impact on Thermal and Cooling Performance

[4]........................................................................................................................5

Figure 6: Thermal Packaging Roadmap 2001-2016 [5] ................................................6

Figure 7: Hot spot cooling by microchannel liquid cooled plate mounted on chip

substrate via TIM layer [6].................................................................................10

Figure 8: High Power IGBT Module [7]. ...................................................................11

Figure 9: Integrated Liquid (R134a) Cooled Plate for IGBT Module [7]. ...................12

Figure 10: Server Rack-Level Cooling for Stacked IGBT Modules [7] ......................12

Figure 11: Two-phase Flow regimes in horizontal channel [20]. ................................30

Figure 12: Taitel-Dukler Flow Regime Map Showing, Stratified, Bubble, Intermittent

and Annular Flow Regimes- 100-micron Channel Dh=200 micron, HFE-7100

Fluid. .................................................................................................................31

Figure 13: Heat transfer coefficient data from Yang and Fujita [37] and Cortina-Diaz

and Schmidt [38] showing the characteristic M-shape behavior [20]. .................33

Figure 14: Two-Phase Microgap Channel Test Apparatus..........................................43

xii

Figure 15: Design Schematics of the Two-Phase Microgap Channel Apparatus .........44

Figure 16: External Water-Cooled Condenser for the two-Phase Microgap Channel

Apparatus. .........................................................................................................45

Figure 17: Pressure Relief Reservoir for the two-Phase Microgap Channel Apparatus.

..........................................................................................................................46

Figure 18: Kobold Flow Meter Calibration Curves for Water and HFE-7100.............47

Figure 19: Intel’s Merom Processor Thermal Test Vehicle (TTV) [51]. .....................48

Figure 20: Intel’s TTV Schematic Three Different Power (Heating) Zones with

Locations of Temperature Sensors. ....................................................................48

Figure 21: Intel’s TTV Serpentine-Type Heating Zones and Locations of Temperature

Sensors [51].......................................................................................................49

Figure 22: Assembled Intel TTV Showing Locations of the Three Heater Zones. ......50

Figure 23: Intel’s TTV Board. ...................................................................................51

Figure 24: TTV Cooper Channel ...............................................................................52

Figure 25: Hermetically Sealed Microgap Channel. ...................................................52

Figure 26: TTV Characteristic Temperature Sensor Calibration.................................53

Figure 27: HFE-7100 Thermal and Fluid Properties [52]. ..........................................58

Figure 28: The CFD Computational Grid...................................................................61

Figure 29: Fluid Channel Grid. ..................................................................................62

Figure 30: Full Conjugate Domain Grid.....................................................................63

Figure 31: CFD Solution Convergence for Key Temperature Sensors........................63

Figure 32: 3-D View of the Microgap Fluid Channel CFD Model..............................64

xiii

Figure 33: XY and YZ Views of the Microgap Fluid Channel CFD Model. ...............65

Figure 34: Model of the Junction Plane Showing the Emulated Serpentine-Type

Heating Zones....................................................................................................66

Figure 35: Effect of Fluid Velocity on Single-Phase Pressure Drop in a 100-micron

Microgap Channel Flowing HFE-7100 (Dh = 200 micron). ...............................72

Figure 36: Effect of Fluid Velocity on Single-Phase Heat Transfer Coefficient in a

100-micron Microgap Channel Flowing HFE-7100 (Dh = 200 micron). P=10W,

Tin=23C. ...........................................................................................................73

Figure 37: Single-Phase Pressure Drop vs. Velocity for HFE-7100 in a 100-micron

Microgap Channel (Dh=200 micron). ................................................................75

Figure 38: Single-Phase Heat Transfer Coefficient vs. Velocity for HFE-7100 in a 100-

micron Microgap Channel (Dh=200 micron). P=10W, Tin=23C........................76

Figure 39: Die Average Sensor Excess Temperature Test Data and CFD Simulation vs.

Velocity, HFE-7100 flowing in a 100-micron Microgap Channel and Uniform

Heating q!=7W/cm2. .........................................................................................79

Figure 40: Conduction Spreading Conjugate Effect on Wall Spatial Heat Flux and

Heat Transfer Coefficient for Uniformly Heated 100-micron Channel with the

Flow of HFE-7100, Tin=23°C, q!=7W/cm2.......................................................84


Heat Transfer Coefficient for Half-Die Heated 100-micron Channel with the Flow

of HFE-7100, Tin=23°C, q!=7W/cm2. ..............................................................85

xiv


Heat Transfer Coefficient for Quadrant-Die Heated 100-micron Channel with the

Flow of HFE-7100, Tin=23°C, q!=7W/cm2.......................................................86

Figure 43: Single-Phase Conjugate Heat Transfer Conversion Rate vs. Fluid Inlet

Velocity for the 100-micron Microgap Channel. P=10W, Tin=23C....................89

Figure 44: Chip Surface (Wall) Temperature Distribution of Uniformly Heated 100-

micron Microgap Channel - (a) 0.7m/s (left), (b) 6.5m/s (right), Tin =23C.........92

Figure 45: Mid-Height Fluid Velocity Vectors Distribution for a 100-micron

Uniformly Heated Microgap Channel - (a) 0.7m/s (left), (b) 6.5m/s (right). .......92

Figure 46: Mid-Height Pressure Distribution for a 100-micron Uniformly Heated

Microgap Channel - (a) 0.7m/s (left), (b) 6.5m/s (right). ....................................93

Figure 47: Chip Surface (Wall) Temperature Distribution of Half-Die Heated 100-

micron Microgap Channel - (a) 0.7m/s (left), (b) 6.5m/s (right), Tin=23C..........94

Figure 48: Chip Surface (Wall) Temperature Distribution of Quadrant-Die Heated

100-micron Microgap Channel - (a) 0.7m/s (left), (b) 6.5m/s (right), Tin=23C...95

Figure 49: Spatial Variation of Heat Transfer Coefficient for Uniformly Heated 100-


Figure 50: Spatial Variation of Heat Transfer Coefficient for Half-Die Heated 100-


Figure 51: Spatial Variation of Heat Transfer Coefficient for Quadrant-Die Heated

100-micron Microgap Channel - (a) 0.7m/s (left), (b) 6.5m/s (right), Tin=23C...97

xv

Figure 52: Pressure Drop vs. Re for a Microgap Channel with Various Channel

Heights, flowing HFE-7100, Tin=23°C, q!=7W/cm2.......................................100

Figure 53: Heat Transfer Coefficient vs. Re for a Microgap Channel with Various

Channel Heights, flowing HFE-7100, Tin=23°C, q!=7W/cm2. ........................101


Heights, flowing Water, Tin=23°C, q!=7W/cm2..............................................102


Channel Heights, flowing Water, Tin=23°C, q!=7W/cm2. ...............................102

Figure 56: Two-phase h vs. q! and x for Uniform Heated 100-micron Channel Flowing

HFE-7100........................................................................................................110


HFE-7100........................................................................................................111


HFE-7100........................................................................................................111

Figure 59: Taitel-Dukler Map with Flow Regimes and h’s for Uniform Heating and

100-micron Channel. G=350, 500, 650, 800, 1000 and 1500 kg/m2s................113

Figure 60: Taitel-Dukler Map with Flow Regimes and h’s for Uniform heating and

200-micron Channel. G=150, 350, 500, 650, 800, 1000 and 1500 kg/m2s........114

Figure 61: Taitel-Dukler Map with Flow Regimes and h’s for Uniform Heating and

500-micron Channel. G=80, 150, 270 and 350 kg/m2s.....................................115

Figure 62: Tabatabai & Faghri’s Modification to the Taitel-Dukler Map Showing the

Proposed Transition Line to Annular Flow [20]. ..............................................117

xvi

Figure 63: Taitel-Dukler Map with Flow Regimes and h’s for Half-Die Heating and

100-micron Channel. G=350, 500, 650, 800, 1000 and 1500 kg/m2s................120


200-micron Channel. G=150, 350, 500, 650, 800 and 1500 kg/m2s..................121


500-micron Channel. G=80, 150, 270 and 350 kg/m2s.....................................122

Figure 66: Taitel-Dukler Map with Flow Regimes and h’s for Quadrant-Die Heating

and 100-micron Channel. G=350, 500, 650, 800, 1000 and 1500 kg/m2s. ........123


and 200-micron Channel. G=150, 350, 500, 650, 800, 1000 and 1500 kg/m2s. 124


and 500-micron Channel. G=80, 150, 270 and 350 kg/m2s. .............................125

Figure 69: Two-Phase h vs. Exit Quality x of the Yang&Fujita [37] and Diaz et al [38]

Data [20]. ........................................................................................................127

Figure 70: Two-Phase h vs. Exit Quality x of the Uniformly Heated 100-micron

Microgap Channel. ..........................................................................................128





Figure 73: Two-Phase h vs. q and x for Half-Die Heating and 100-micron Channel.131


xvii


Figure 76: Two-Phase h vs. q and x for Quadrant-Die Heating and 100-micron

Channel. ..........................................................................................................133


Channel. ..........................................................................................................133


Channel. ..........................................................................................................134

Figure 79: Two-Phase Heat Transfer Coefficient versus Retp for the Uniformly

Heated 100-micron Microgap Channel.............................................................138

Figure 80: Characteristic Heat Transfer Coefficient Curve with Illustrated Ranges of

Pseudo Annular and Pseudo Intermittent Flow Regimes, Uniformly-Heated 100-

micron Channel, G =1500 kg/m2s....................................................................143

Figure 81: Inversely Calculated Spatial Heat Transfer Coefficient for 100-micron

Channel and Uniform Heating. 25W, G= 1500 kg/m2s. ...................................150


Channel and Half-Die Non-Uniform Heating. 25W, G= 1500 kg/m2s..............151


Channel and Quadrant-Die Non-Uniform Heating. 25W, G= 1500 kg/m2s. .....152

Figure 84: Inversely Calculated Chen-based Spatial Heat Transfer Coefficient for 100-

micron Channel and Uniform Heating. 25W, G= 1500 kg/m2s. .......................154

Figure 85: Inversely Calculated Chen-based Spatial Heat Transfer Coefficient for 100-

micron Channel and Half-Die Non-Uniform Heating. 25W, G= 1500 kg/m2s..155

xviii

Figure 86: CFD Temperature Distribution vs. Conduction-Only Based Modeling with

Wall-Prescribed Average Chen-Based h. 25W, G= 1500 kg/m2s. ....................157

1

Chapter 1:

Trends and Cooling Requirements in the Electronic Industry

In recent decades the industry-wide trend in electronics has been toward greater

compactness, functionality and feature count and thus power dissipation for nearly all

the categories of electronic equipment. The International Electronics Manufacturing

Initiative (iNEMI) projects the chip power and chip heat flux trends for various

electronic enclosure form factors, from servers to notebook platforms. Figure 1 shows

the iNEMI’s view of chip power chip flux trends for server platforms [1]. It is quite

clear from the figure that the market shall, if it has not already, experience

unprecedented growth in chip power and heat flux that by 2012 could reach 300W and

150 W/cm2 in heat dissipation and heat flux, respectively.

Figure 1: iNEMI’s Server Chip power and Heat Flux Trends [1].

2

Although the increased awareness of power consumption and efforts to develop more

energy efficient devices will cause this rate to slow, as per the International

Technology Roadmap for Semiconductor (ITRS) shown in Figure 2, for the cost-

performance system category, this slow down might not become apparent until the

year 2015 [2]. On the other hand, changes in chip layout and packaging technologies,

throughout recent years, have led to the wide adoption of flip chip technology and the

appearance of highly non-uniform chip power dissipation. Both of these trends have

had a strong impact on thermal management needs and thermal design constraints on

advanced chip packages.

Figure 2: ITRS Power Trend for High Performance and Cost Performance

Electronic Chips [2].

3

As shown in Figure 3, in the past decade thermal management of flip chip dies with

non-uniform power dissipation has focused on the need to significantly lower the

maximum chip-to-heat sink thermal resistance. Continuously improving heat sink

performance has

made the chip-to-heat sink resistance dominant and the “controlling” or critical

element of the total system thermal resistance [3]. Efforts must thus be directed at

minimizing the chip-to-sink thermal resistance. Note that the arrow and circle in

Figure 3 refer the thermal resistance curve to the year 2005, when the reference was

published.

Figure 3: Trends in Chip Package Thermal Resistance [3].

The issue of chip power non-uniformity or non-uniform die heat flux is a frequent

subject of the recent electronics cooling literature [4]. Figure 4 displays the heat flux

4

distribution on a Pentium III and Itanium chip, respectively, and shows how silicon

architecture, design styles and complexity affect the power gradient across the die.

While “hot spots” on the Intel Itanium processor can reach heat fluxes of 300 W/cm2

[4], the Pentium III peak flux is close to just 50W/cm2.

Figure 4: Power Non-Uniformity of Intel’s Itanium Processor [4]

The impact of such on-chip hotspots, or high heat flux concentrations at the die

junction plane, can be severe. This is clearly illustrated in Figures 5 where the thermal

impact of power non-uniformity, or the presence of a hot spot, on the peak temperature

rise is assessed. It is seen that the non-uniform distribution could, for the conditions

examined, be equal to having an additional dissipation of about 30W, uniformly

distributed, from the perspective of the overall thermal resistance and chip thermal

management potential. [2,5]. Researchers and designers, faced by these challenges,

have been focusing on more efficient thermal management techniques and alternative

5

approaches to smooth the temperature distribution resulting from the highly non-

uniform die heat flux.

Figure 5: Power Map (Non-Uniformity) Impact on Thermal and Cooling

Performance [4].

As a consequence, the thermal packaging community started searching for and

investigating new cooling technologies for high heat flux chips, as depicted in Figure 6.

While the initial efforts in the 2000-2005 time frame, associated with the transition to

130nm and later to 90nm features, involved improvements in the Thermal Interface

Materials (TIMs), wafer thinning is a promising approach to reducing the thermal

6

resistance for chips with 65nm features. However, as the chip features continue to

shrink towards 45nm and the chip power and heat flux increase towards 225W and

450W/cm2, respectively, there is an urgent need for advanced thermal management

techniques. This thermal management roadmap does suggest that for the 2013 and

beyond, when chip heat flux might exceed 500W/cm2, two-phase cooling by direct

contact of an evaporating/boiling dielectric liquid with the chip might be the only

viable thermal management solution. [5].

Figure 6: Thermal Packaging Roadmap 2001-2016 [5]

Dissertation Roadmap

The present study focuses on the two-phase thermal performance limits of non-

uniformly heated microgap channels in a packaged chip-scale form factor. The

research goal is to study the thermal performance of such microgap channel coolers in

a non-ideal form factor with non-uniform heating conditions and to use the results to

7

provide the technical foundation for the engineering, design of such microgap channel

coolers applied to single chips and also to 3D modules containing multiple chip stacks.

While Chapter 1 provided an introduction to recent and future trends of cooling

requirements in the electronics industry, Chapter 2 covers a literature review of liquid

cooling of electronic modules. Chapter 3 provides the theoretical background for

single-phase and two-phase thermofluid characteristics in miniature channels. Chapter

4 provides a detailed description of the experimental apparatus used to conduct the

two-phase as well as single-phase experimental tests on the 100-, 200- and 500-micron

channels used in the present work. Chapter 5 covers the details of the CFD based

numerical model and simulations used to validate and enhance the experimental test

data. Chapter 6 discusses the single-phase test data comparisons with available

correlations and with CFD model results. The chapter also provides an overall

assessment of the single-phase thermal performance of the various microchannels used

in the study with HFE-7100 and water as the working fluid. Chapter 7 covers the two-

phase data and discussion, including heat transfer characteristics and flow regime

modeling. Chapter 8 discusses the experimental data comparison with heat transfer

correlations in the literature for the Annular and Intermittent flow regimes. This

chapter also covers the utilization of CFD for the inverse calculations of spatial heat

transfer coefficient and introduces a simple semi-numerical approach for the prediction

of wall temperature distribution and hot spots of non-uniform heating.

8

Chapter 2:

Liquid Cooling of Electronic Modules – Literature Review

2.1 Introduction

Thermal management needs of the electronics industry continue to be driven by the

demand for increased functionality, high heat dissipation and density, component

miniaturization, and the reliability benefits of junction temperature reduction and

control.

Advanced liquid cooling thermal management techniques for electronics can be

classified as direct or indirect methods; depending on whether, the cooling fluid is in

direct contact with the electronic module chip package. Single-phase and two-phase

liquid cooled microchannels are examples of indirect liquid cooling while pool boiling

and liquid immersion provide good examples of direct liquid cooling. While one of the

main benefits of direct liquid cooling is the elimination of the contact thermal

resistance between the cooling module and the surface of the electronic chip, these

techniques involve intensive reliability packaging and assembly and maintenance

requirements. Nevertheless, this direct method, from a packaging perspective, is

efficient for cooling 3D or multi-chip stacked modules. Active (pumped) liquid

cooled microchannels while they are indirect methods, can provide extensive wetted

surface area for the liquid to interact with in both single- or two-phase regimes. They

9

also constitute very good methods for cooling single chips such as advanced

microprocessors and graphics chips.

2.2 Microchannel Coolers

Active liquid cooling has started to emerge as a feasible solution for even cost

performance electronics systems. The recent increase in CPU heat fluxes coupled with

the need to thermally design for the highest possible heat flux for speed reasons,

caused thermal system to become more complex and has paved the way for active

cooling. High power density cores on the die necessitate the use of active

micromechanical means for heat removal [3].

Figure 7 shows that the use of single-phase microchannel liquid cooling can be an

effective means to overcome the die hot spot problem and achieve acceptable junction

temperatures [6]. However, this method did not eliminate the large TIM thermal

resistance between the die and the first layer of microchannel assembly.

10

Figure 7: Hot spot cooling by microchannel liquid cooled plate mounted on chip

substrate via TIM layer [6]

Figures 8 and 9 display successful implementations of two-phase liquid cold plates for

industrial power electronics systems [7] such as Integrated Gate Bipolar Systems

(IGBT’s). The pumped two phase cooling achieved around 50% increase in power

dissipation compared to single phase and 120% increase in power dissipation

compared to air cooling. The physical volume reduction achieved with the two-phase-

cooled system is significant and even provides a modest cost reduction versus the air-

cooled system. The use of a vaporizable dielectric fluid, R134a indirectly contacting

the chips, operating at its saturation temperature, allows the use of a smaller quantity

of liquid, a smaller pump for low-flow operation, and smaller tubing diameters, when

11

compared to a comparable single-phase water cooling system designed for use within

the same type of cabinet (shown in Figure 10) and to dissipate the same module heat

loads. The use of a vaporizable dielectric fluid in a copper cold plate with convoluted

fin internal structure is demonstrated to yield around 100% additional capacity to

dissipate heat generated at the IGBT module base, as compared to the water-cooled

cold plate tested; the improvement over the production air-cooled finned aluminum

extruded thermal solution is demonstrated to be greater than 125% [7].

Figure 8: High Power IGBT Module [7].

12

Figure 9: Integrated Liquid (R134a) Cooled Plate for IGBT Module [7].

Figure 10: Server Rack-Level Cooling for Stacked IGBT Modules [7]

2.3 Pool boiling

Pool boiling as a method for cooling electronic modules can provide much higher

performance than conventional forced air [8], Furthermore, understanding pool boiling

is important for the successful implementation of immersion cooling.

You et al, [9] discussed a method for enhancing boiling heat transfer. The method of

particle layering is introduced as an effective and convenient technique for enhancing

boiling heat transfer on a surface. Such an enhanced surface, showed a decreased level

13

of wall superheat under boiling and an increased critical heat flux relative to superheat

and critical heat flux values for an untreated surface, due perhaps to an increased

number of nucleation sites or to a change in cooling modalities to two-phase flow in a

porous layer. Application of this technique results in a decrease of heated surface

temperature and a more uniform temperature of the heated surface; both effects are

important in immersion cooling of electronic equipment.

Arik and Bar-Cohen [8], showed that boiling heat transfer with the candidate liquids

provides heat transfer coefficients that are as much as two orders of magnitude higher

than achievable with forced convection of air. Unfortunately, the highly effective

nucleate boiling domain terminates at the Critical Heat Flux, approximately in the

range of 20 W/cm2 at atmospheric conditions and saturation temperature.

Consequently, if immersion cooling is to be used, ways must be found to increase the

pool boiling CHF of these dielectric liquids. Use of a pool boiling CHF correlation

points to the possibility of reaching a CHF of nearly 60 W/cm2, using elevated

pressure and subcooling, along with a dilute mixture of a high boiling point

fluorocarbon, and applying a microporous coating to the surface of the chip.

Bergles and Kim [10], demonstrates that the generation of vapor below a heated

surface is an effective means of reducing the large superheat required for inception of

boiling with liquids suitable for direct immersion cooling of microelectronic devices.

In the experiments with R-113 and a plain copper heat sink surface, the incipient

boiling superheat was reduced from 33 K to as low as 8 K. With a sintered boiling

surfaces, the incipient boiling superheat was reduced from 22 K to as low as 7 K. A

14

reasonable explanation for the effectiveness of this sparging technique is that the

impacting bubbles activate temporarily dormant cavities that, in turn, activate large

neighboring cavities. The technique appears to be easily adaptable to liquid

encapsulated modules containing arrays of microelectronic devices.

Normington et al [11], demonstrated experimental results related to the use of mixtures

of dielectric liquids to control temperature and overshoot while handling high heat

fluxes. A variety of pure dielectric liquids from Ausimont (boiling points from 81 to

110°C) were evaluated. These liquids are similar to Fluorinert liquids from 3M. Data

have been taken on single pure liquids showing the usual expected substantial

overshoot (26’C average) during the incipience of nucleate boiling. The addition of a

second liquid to modulate the temperature and control the overshoot has been

presented. Various mixtures (20-95% of low boiling point; 580% of high boiling point)

were then tested with some mixtures showing virtually no overshoot (0-6 °C) while

still allowing high total heat fluxes greater than 30 W/cm2. On average, the overshoot

was reduced from 26 to 4°C for a variety of liquid mixtures. Some mixtures allowed

for zero overshoot. The 4°C overshoot was less than the temperature variation across

the chip. The effect of liquid mixtures in reducing overshoot is pronounced only in the

high subcooling case (50°C subcooling); for 10°C subcooling, the effect is

insignificant. The mechanisms of these results are not clear. It is, however, clear that

relatively small amounts of a second liquid can strongly modify the boiling heat

transfer characteristics of the dielectric liquids.

15

2.4 Liquid Immersion Cooling

Liquid immersion cooling represents a potential method for meeting the requirements

for removal of increasingly high heat fluxes from individual chips and from three-

dimensional microelectronic packages. Kraus and Bar-Cohen [12] and Bar-Cohen et al

[13], provide a detailed analysis on Liquid immersion cooling of microelectronic

systems, many researchers investigated various aspects of liquid immersion cooling

focusing on 3D modules. The electronic module’s external surface temperature

(condenser temperature) is a crucial aspect in the success of a liquid immersion

technique as it limits the ability of the module’s surface to expel thermal energy

outside the system.

Yokouchi et al [14], presents a cooling techniques using direct immersion cooling for

high-density packaging and provides a discussion focusing on a) the treatment of

bubbles produced by nucleate boiling and b) the control of coolant composition to

prevent “temperature overshoot” occurring at the boiling point as thermal hysteresis.

Maintaining subcooled boiling (the initial stage of nucleate boiling) up to the

maximum power of the application is a useful technique in high-density packaging of

computers because this technique produces fewer problems than saturated boiling.

Using a coolant that mixes two fluorocarbons having different boiling points at a ratio

of 80%-20% was found to prevent temperature overshoot on the chip surface.

The adoption of direct immersion cooling of microelectronic chips and other devices

16

has been hampered by lack of understanding of, and inability to control, the

temperature overshoot or high wall superheat associated with the inception of nucleate

boiling.

2.5 Liquid Immersion Modules

Ciccio and Thun [15], showed that ebullient cooling with FC-78 refrigerant provided

excellent cooling for an ultra-high density VLSI module mounted in a sealed container

for condenser temperatures between 70F and 90F. They were able to double the

module power density sustainable with conventional (forced air) cooling techniques.

At a time when most chips were dissipating less than 1W, it was possible to maintain a

2W/chip and 15 W/in2 (2.35 W/cm2) while keeping junction temperatures blow 150F.

(65.6 0C)

Lee et al, [16] demonstrated experimentally the capability of liquid-encapsulated

system to cool a multi-chip module (MCM) package. Tests were performed on both

dry (no liquid-filled) and liquid-filled packages. In the liquid-filled situation, either a

pure dielectric liquid or a dielectric liquid mixture was employed. The MCM package

was externally cooled by either free-air or forced-air (1.0 to 2.54 m/s of air flow). Heat

transfer history from single-phase, through nucleate boiling, to film boiling was

documented.

The overall improvement for the liquid-filled package was 2–4 times compared to the

dry package, due to the superior thermal properties of dielectric liquids compared to

air. The maximum power dissipation in the liquid-filled package at 2.54 m/s external

17

airflow was 18 W (based on junction temperature maximum of 125C). In the liquid-

filled package, both the single-phase and boiling heat transfer were enhanced by

varying the external boundary conditions from free-air to forced-air.

The total power dissipation limit in the liquid-filled package is strongly influenced by

the ability to condense the vapor in the package. By changing the boundary conditions

from free-air to forced-air (2.54 m/s), the condenser (top lid) efficiency is raised, thus

raising the maximum power dissipation by 2.5 times. Results also indicated that for

any given external boundary condition, the allowable power dissipation did not vary

much under different liquid conditions: non-degassed liquid, degassed liquid at slightly

above ambient pressure, and degassed liquid at ambient pressure. When the system

was sealed, increasing power in the package created large liquid pressure and raised its

boiling point. The chips remained in the single-phase regime and no boiling occurred.

The paper also studies the effect of coolant mixture of two fluids, D80/HT110

(50/50% by volume). The mixture boiling curve behaved differently than the single-

liquid curve: it had a long path of partial boiling and did not reach film boiling as

junction temperature reached 125C. This particular mixture showed less-efficient

boiling heat transfer than the single liquid. However, a proper composition of the

mixture may raise the allowable power in the module compared to the single liquid,

while maintaining the average junction temperature below 125 C. With a small-scale

package (such as in the present study), when the system was sealed (with pure liquid),

increasing power in the package created large liquid pressure and raised its boiling

point. Due to the high boiling point, the dies remained in the single-phase regime.

18

Nelson et al, [17] describes a multi-chip module (MCM) package that uses integral

immersion cooling to transfer heat from the chips to a final heat transfer medium

outside the package. The package is a miniature immersion cooled system with a pin-

fin condenser that can be operated in either the submerged or vapor-space condensing

mode. Tests have been performed with the module fully powered and with subsets of

the chips powered. The results indicate that the heat transfer coefficient is similar in all

partially powered modes. The paper shows that immersion cooling with Fluorinert

FC72 is a viable method of thermally linking the chips in an MCM to an overhead heat

exchanger, competitive in thermal resistance with both through-substrate cooling and

direct above-substrate cooling.

Geisler el al [18], in their paper, explored the viability of passive liquid cooling to

meet the needs of future VME-size electronics modules. Chip heat fluxes in excess of

20W/cm2 were achieved while maintaining chip temperatures below 110°C. Further,

an overall module heat dissipation of 124W was transferred with 80°C module edge

temperatures (FC-72, 3atm, finned module cover). The thermal performance of the

module was limited by the presence of a bubble-fed vapor/air gap that reduced the

ability of the module cover to extract heat from the liquid and threatened to burn out

nearby components as it grew.

2.6 Flow Boiling

Microgap coolers provide direct contact between chemically inert, dielectric fluids and

the back surface of an active electronic component, thus eliminating the significant

19

interface thermal resistance associated with thermal interface materials and/or solid-

solid contact between the component and a microchannel cold plate. On the other hand,

the very good thermal performance, represented by the flow boiling, especially with

annular-flow regime, high heat transfer coefficient, makes the concept of microgap

cooler an appealing one for scholars in the thermal packaging community.

Kim et al [19], provided an exploratory study of the thermofluid characteristics of two-

phase microgap coolers flowing FC-72 in asymmetrically and uniformly heated

channels. Taitel and Dukler flow regime mapping methodology suggested that

intermittent and annular flow regimes dominated the behavior of their 110 micron and

500 micron channels. Their data revealed that area-average heat transfer coefficients

between 7.5 kW/m2K and 15.5 kW/m

2K, can be attained for microgap channels of 110

micron and 500 micron respectively. Heat transfer coefficient data was well bounded

by the predictions of the Chen and Shah correlations for the Annular and Intermittent

flow regimes, respectively.

Rahim et al [20], provided detailed analysis of microchannel/microgap heat transfer

data for two-phase flow of refrigerants and dielectric liquids, gathered from the open

literature and sorted by the Taitel and Dukler flow regime mapping methodology.

Annular flow regime was found to be the dominant regime for this thermal transport

configuration and its prevalence is seen to grow with decreasing channel diameter and

to become dominant for refrigerant flow in channels below 0.1 mm diameter. A

characteristic M-shaped heat transfer coefficient variation with quality (or superficial

velocity) for the flow of refrigerants and dielectric liquids in miniature channels has

20

been identified. Comparison of the microgap refrigerant data to existing classical

correlations reveals that the Chen correlation provides overall agreement to within a

standard deviation of 38% for the entire data set. However, classification of the data by

flow regime does allow for improved predictive accuracy.

Microgap channel coolers flowing two-phase dielectric fluid have a good potential for

cooling advanced high power electronics for they provide good thermal performance

and eliminate the inherited TIM thermal resistance prevailing with indirect liquid

cooling techniques. They also can be considered as cost effective and reliable

technique compared to the expensive microchannel coolers. In order, however, to

address the particular applications in the industry for such microgap channel coolers, a

focus should be on detailed study of the two-phase performance characteristics under

non-ideal conditions including short channel length, non-uniformly heated channels,

conjugate heat transfer effect and packaging in a chip-scale form factor. The present

work focuses on studying and modeling the two-phase characteristics of microgap

channels under these practical non-ideal industry parameters.

21

Chapter 3:

Theoretical Background

3.1 Single-phase Thermofluid Characteristics in miniature channels

The concept of a microgap is a promising cooling technique for advanced

microelectronics. Microgap channels require no thermal interface attachments and thus

allow for the direct and efficient of transfer heat directly form the chip surface. An

appropriate design of a microgap requires knowing the pressure drop and overall

thermal performance, as these two engineering parameters are important to size up the

microgap and the pumping power associated with it.

3.1.1. Pressure drop correlations

Thome [21], in his Wolverine’s Engineering Data Book lists numerous literature

correlations of single-phase pressure drop. Garimella and Singhal [22], showed that

conventional correlations for laminar and turbulent flow adequately predict the

behavior in microchannels of hydraulic diameters as small as 250 µm.

Classical single-phase flow correlations for the pressure drop in parallel plate channel

by Kays and London [23] can be expressed as:

22

!

"P =#V 2

21$% c

2( ) + Kc{ } + 4 & fL

Dh

$ 1$% e

2( ) + Ke{ }'

( )

*

+ , (3.1)

Where

!

"V 2

2

is the dynamic pressure associated with flow in the channel,

!

"c

= Ac/A

in

and

!

"e

= Ac/A

out are the area ratios of contraction and expansion of the flow at the

channel entrance and exit, respectively.

!

Kc and

!

Ke are the loss coefficients of flow

irreversibilities and f is the friction factor representing the channel friction losses.

Shah and London [24] correlated the friction factor f in a parallel plate for laminar

developing flow in the form of:

( )( )( )

Re/

000029.01

44.3

4

674.024

44.3

2

2/1

2/1

!!!!

"

#

$$$$

%

&

'+

('

+

+=(+

++

+ x

xx

xf (3.2)

where x+ is the dimensionless hydrodynamic axial distance, which can be expressed

by:

!

x+

=x /D

h

Re (3.3)

23

In the fully developed laminar flow, i.e. for x+> 0.05, the friction factor reaches an

asymptotic value or f = 96/Re.

3.1.2. Heat transfer correlations

The thermal performance of a microgap channel is evaluated using the dimensionless

Nusslet number as given by:

!

Nu =h.D

h

k (3.4)

Where h is the heat transfer coefficient,

!

Dh is the channel hydraulic diameter and k is

the fluid thermal conductivity and h is the heat transfer coefficient. The heat transfer

coefficient is defined as:

!

h =q

A"T (3.5)

Where

!

"T is the temperature difference between the channel heated surface (wall) and

the cooling fluid, A is the wall surface area and q is the wall heat transfer rate that can

be determined from implementing the channel energy balance equation via:

(3.6)

24

!

q = m•

Cp (Toutlet "Tinlet )

Where

!

m

•

the channel fluid mass flow rate,

!

Cp is the fluid specific heat and

!

Tinlet

and

!

Toutlet

are the channel fluid inlet and outlet temperatures, respectively.

Wolverine’s Engineering Data Book [21], lists numerous literature correlations of

single-phase Nusslet number for a variety of flow types including laminar and fully

developed turbulent flow.

Garimella and Singhal [22], showed that conventional correlations for fluid flow and

heat transfer adequately predict the behavior in microchannels of hydraulic diameters

as small as 250 µm.

Kays and Crawford [25], reviewed many Nusslet number equations available in the

literature for circular tubes, circular tube annuli and rectangular tubes for laminar flow

and thermally fully developed or developing flow with uniform surface temperature

and uniform surface heat flux boundary conditions. Among them, and more directly

related to the channel conditions in the present study, is the Nusslet number for

laminar developing flow in parallel plate channels with isoflux boundary conditions as

!

Nu = 8.24 +0.065(D

h/L)RePr

1+ 0.04[(Dh/L)RePr]

2

3

(3.7)

25

where the value of 8.24 represents Nusslet number for the fully developed laminar

flow.

In the fully developed turbulent flow, Dittus and Boelter equation [25] can be used for

Re>10,000 and is given by

!

Nu = 0.023Re0.8Pr

0.4 (3.8)

More specifically related to the characteristics of the channel type considered in the

present work, Kakac and Shah [26] predicted the local and mean heat transfer

coefficients in uniform heat flux, asymmetrically-heated, parallel plate channels as

follows:

( ) 1

122

*224exp

6

1!

"

=

#$

%&'

( !!= )n

x

n

xnNu

*

* (3.9)

( ) 1

122

*224exp1

6

1!

"

=

#$

%&'

( !!!= )n

m

n

xnNu

*

* (3.10)

Where the dimensionless axial distance is given by:

26

PrRe

/* hDL

x = (3.11)

3.1.3 Effect of heating non-uniformity

It is important to note the lack of available literature and correlations for non-uniform

heat flux in refrigerant-cooled in micro channels. Remley, et al [27], experimentally

investigated turbulent wall friction and forced convection heat transfer in a water-

cooled trapezoidal channel with high Reynolds numbers and 1.14 cm hydraulic

diameter. The paper reported that the Colebrook correlation [25] predicted the

unheated channel friction factors well. It, however, systematically over predicted the

measured friction factors obtained with the test section non-uniformly heated test

section. Perimeter-average convective heat transfer coefficients for laterally non-

uniform imposed heat fluxes were compared with the predictions of three widely-used

correlations for turbulent flow in circular channels. All the correlations under predicted

the data, typically by 11–28%. Although the form factor in Remley, et al’s study is

larger than in the present study, the paper nonetheless discussed an important factor

that is the effect of heating non uniformity on the accuracy of correlations in predicting

pressure drop and thermal performance of studied channels.

3.2 Two-phase Thermofluid Characteristics in miniature channels

3.2.1 Introduction

27

The research community had classified micro channels under different categories with

different definitions. Mehendale et al [28], proposed a purely geometric definition,

ignoring any impact of fluid properties, and considered passages in the diameter range

from 1 micron to 100 micron as micro-channels, 100 microns to 1 mm as meso-channels,

1 mm to 6 mm as compact passages, and greater than 6 mm as conventional passages.

Kandlikar and Grande [29], classified micro channels based on fabrication technology.

They proposed that channels with hydraulic diameters of 3 mm or larger be considered as

conventional, channels with a hydraulic diameter range of 200 micron to 3 mm to be

classified as mini-channels, and, as new technologies were needed to create passages with

diameters below 200 micron, such channels would be defined as micro-channels.

Considering that severe rarefaction effects for many gases are encountered between 10

micron and 0.1 micron, and that such effects might become pronounced in two-phase

flow, Kandlikar and Grande referred to this as the transitional region and used 10

microns as the lower limit on micro-channel behavior.

Kew & Cornwell [30] used the so-called confinement number, defined as the ratio of the

theoretical departing bubble diameter to the channel diameter, i.e.,

!

Co =[" /(g(#l $ #v ))]

d (3.12)

to define the transition to micro-channels flow. Based on a statistical analysis of two

phase heat transfer coefficient data and comparison to correlations provided by Liu and

28

Winterton [31], Cooper [32,33], Lazarek and Black [34], and Tran et al [35], Kew and

Cornwell determined that, for confinement numbers greater than 0.5, the measured heat

transfer coefficients departed significantly from the values predicted by the relevant

conventional channel correlations. They thus chose Co= 0.5 as the transition criteria for

micro-channel behavior. It is interesting to note that, in the present study, the confinement

number Co takes the values of 4.6, 2.3 and 0.93 (all higher than 0.5) for HFE-7100 with

100-, 200- and 500-micron channels, respectively.

Forced flow of dielectric liquids with phase change in heated microgap channels had

been recently the subject of many researches especially in the chemical, nuclear and

mechanical engineering fields. Although the present study focuses the thermal

characteristics of a chip-scale non-ideal and very short uniformly heated microgap

channel with dielectric fluid HFE-7100, it is nonetheless, worth summarizing some of

the available research data on similar refrigerants, flow or geometry parameters. Lee

and Lee [36], investigated two-phase heat transfer in a 300mm long and 20mm wide

horizontal rectangular gap with hydraulic diameters of 0.8mm-3.6mm using R113

refrigerant. They reported the dominance of the annular flow regime and gathered 491

heat transfer coefficient data points in the range of 5 kW/m2K for a mass flux range of

52-208 Kg/m2.s with total pressure drop of 40 kPa. Yang and Fujita [37] used R113 in

a similar but somewhat shorter, 100mm long and 20mm wide horizontal rectangular

gap with hydraulic diameter of 0.4 mm-3.6 mm. Their 292 data points reported heat

transfer coefficients of up to 6 kW/m2K for mass fluxes in the range of 100 Kg/m

2s

29

subject to a heat flux of 2 W/cm2 heat flux. Cortina-Diaz and Schmidt [38]

investigated flow boiling heat transfer using n-Hexane and n-Octane in a 12.7mm by

0.3 mm channel with 0.6 mm hydraulic diameter. They reported heat transfer

coefficient of 6 kW/m2K in the range of a 100 Kg/m

2s mass flux and 2-4 W/cm

2 heat

flux.

Madrid et al. [39] explored the behavior of HFE-7100 in a 40 parallel channel vertical

rectangular channel mini cooler. The channels were 220mm long with a 0.84mm

hydraulic diameter. Their 258 data points indicated a highest heat transfer coefficient

value of 5.7 kW/m2K at 71-191 Kg/m

2s mass flux range and 0.17-0.46 W/cm

2 heat

flux range. A common conclusion from these studies is the heat transfer coefficient

limit of around 6 kW/m2K at the range of 50-200 Kg/m

2s mass flux and subject to low

heat flux of 1-2 W/cm2. The present study focuses on a larger range of mass fluxes of

up to 1500 kg/m2s and heat fluxes up to 50 W/cm

2.

3.2.2. Two-phase flow regime modeling

The flow of two-phase (vapor and liquid) mixture in pipes or channels has special

characteristics and can take different forms, i.e., flow regimes, depending on the distinct

vapor/liquid distributions. Four primary two-phase flow regimes, namely, Bubble,

Intermittent, Stratified and Annular, as well as numerous sub-regimes, have been

identified in the literature [20]. Bubble flow is associated with uniform distribution of

small spherical bubbles within the liquid phase. Intermittent flow is characterized by the

flow of liquid plugs separated by elongated slug-shape gas bubbles. Stratified flow is

30

characterized by the liquid flowing along the channel’s lower surface and vapor flows

above. Annular flow occurs when the liquid flows in a thin layer along the channel walls

while the vapor flows in the channel center creating a vapor core. These flow regimes are

graphically shown in Figure (11) as they progress axially along a horizontal channel

length.

Figure 11: Two-phase Flow regimes in horizontal channel [20].

While the literature contains many approaches to mapping these vapor/liquid flow regimes

and makes use of various two-phase thermo-fluid parameters, Taitel and Dukler [40]

pioneered physics-based flow regime mapping using first-principle, analytical equations.

Their approach most often represented on coordinates of liquid and vapor superficial

velocity, respectively, has continued to evolve [41] and is today widely used for predicting

and analyzing two-phase flow in tubes and channels.

The Taitel and Dukler (TD) map of two-phase flow in pipes identifies the boundaries

among the four dominant flow regimes, i.e., stratified, intermittent, bubble and annular.

The TD flow regime map schematically shows, in Figure (12), for the 100-micron channel

with hydraulic diameter Dh of 200 micron, flowing HFE-7100 fluid, used in the present

study, the four flow regimes along with transition lines between one regime and another as

31

relative functions of the liquid and vapor superficial velocities. The stratified flow regime

occupied the lower corner of the map at low superficial vapor velocity and low superficial

liquid velocity. Moderate superficial liquid velocity leads to intermittent flow while further

increase in superficial liquid velocity, at similar low superficial vapor velocity leads to

bubble flow. Annular flow occupies the right triangle-shape part of the map as both

superficial gas and liquid velocities increase from their values at bubble and intermittent

flow regimes.

Figure 12: Taitel-Dukler Flow Regime Map Showing, Stratified, Bubble,

Intermittent and Annular Flow Regimes- 100-micron Channel Dh=200 micron,

HFE-7100 Fluid.

These transition lines reflect the distinction between surface tension driven regimes, such

as bubble and intermittent flows, and shear force driven regimes, such as stratified and

32

annular. Furthermore, the TD flow regime map relies on adiabatic models that ignore the

thermal interactions between phases, the pipe and the environment all of which are present

in the diabatic systems. This dependence of adiabatic models makes the transition lines of

the TD model less accurate when high heat fluxes are applied at the channel/pipe wall

[42].

In addition to the TD flow regime map, other analytical approaches of flow regime

transitions are available in the literature. Amongst them are the Weismann et al method

[43], and Tabatabai and Faghri method [44] that proposed a modification to the TD map

based on a criterion for the transition from surface tension dominated behavior to shear

dominated behavior. These approaches compliment the traditional empirical flow regime

maps obtained for water-steam, and other industrial fluids and cannot be easily

extrapolated to microchannels and refrigerants.

Rahim and Bar-Cohen [20] conducted a detailed analysis of microchannel and microgap

heat transfer data for two-phase flow of refrigerants and dielectric liquids, gathered from

the open literature and sorted by the Taitel and Dukler flow regime mapping methodology,

reveals the existence of the three primary flow regimes, i.e. Bubble, Intermittent, and

Annular, along with Stratified flow for horizontal configurations, in miniature channels.

However, the annular flow regime is found to be the dominant regime for this thermal

transport configuration and its prevalence is seen to grow with decreasing channel

diameter and to become dominant for refrigerant flow in channels below 0.1mm diameter.

33

3.2.3. Characteristics of two-phase heat transfer in micro channels

The literature data of two-phase heat transfer coefficients suggest a characteristic M-

shaped heat transfer coefficient variation with quality (or superficial velocity) for the

flow of refrigerants and dielectric liquids in miniature channels. The inflection points

in this M-shaped curve are seen to equate approximately with flow regime transitions,

including a first maximum at the transition from Bubble to Intermittent flow and a

second maximum at moderate qualities in Annular flow, just before local dryout

begins. This characteristic behavior is shown in Figure 13, taken from the

comprehensive work done by Rahim et al [20], on the data from Yang and Fujita [37]

and Cortina-Diaz and Schmidt [38].

Figure 13: Heat transfer coefficient data from Yang and Fujita [37] and Cortina-

Diaz and Schmidt [38] showing the characteristic M-shape behavior [20].

34

3.2.4. Heat Transfer Correlations

Thome and Collier, in their book [45], discussed the classical two-phase heat transfer

correlations available in the literature and identified the prominent role played by the

two-phase Reynolds number, based on the liquid fraction of the mass flux in the

channel, in attempts to correlate the two-phase heat transfer coefficient. Kim, et al [19],

analyzed two-phase microgap heat transfer in simple geometries and correlated to

Chen and Shah correlations. Rahim and Bar-Cohen [20] conducted detailed analysis of

microchannel/microgap heat transfer data for two-phase flow of refrigerants and

dielectric liquids, gathered from the open literature. They analyzed the predictive

accuracy of five classical two-phase heat transfer correlations [45] for miniature

channel flow was examined. These classical correlations include Chen [46], Kandlikar

[47], Gungor-Winterton [48], Gungor-Winterton Revised [49] and Shah correlations

[50]. Selecting the best fitting of the classical correlations for each of the flow regime

categories is seen to yield predictive agreement with regime-sorted heat transfer

coefficients that does not depart significantly from the agreement found in large pipes

and channels.

Comparison of a sample of microgap refrigerant data to existing classical correlations

reveals that the Chen correlation provides overall agreement to within a standard

deviation of 38% for the entire data set [20]. However, classification of the data by

flow regime does allow for improved predictive accuracy. The authors have shown

that the dominant, low quality Annular data could be correlated by the Chen

35

correlation to within an average discrepancy of just 24%, while the Shah correlation

provides agreement to within an average discrepancy of 32% (vs. 72% for Chen) for

data in the Intermittent regime, and the modified Gungor-Winterton correlation to

approximately 37% (vs. 39% for Chen) for the moderate-quality annular flow data.

In the present work, the two correlations for two-phase flow heat transfer prediction,

namely, the Chen and Shah correlations, were used as reference points to compare

against the various experimental data obtained.

Chen Correlation

The starting point for the Chen correlation is:

!

h = hmic

+ hmac

(3.13)

The macroscopic contribution was calculated using the Dengler Addoms correlation

with a Prandtl number correction factor to generalize the correlation beyond water as

the working fluid.

!

hmac

= hlF X

tt( ) (3.14)

Here F is an acceleration factor and the single phase liquid-only convective coefficient

(hl) is calculated via the Dittus-Boelter equation:

36

4.08.0PrRe023.0ll

l

l

D

kh !

"

#$%

&=

(3.15)

where

( )

l

l

DxG

µ

!=

1Re

(3.16)

The microscopic contribution was calculated using the Forster-Zuber correlation for

pool boiling with an additional correction factor in the form of a suppression factor, S:

( )[ ] ( )[ ] SPTPPTTh

ckh lwsatlsatw

vlvl

lpll

mic

75.024.0

24.024.029.05.0

49.045.079.0

00122.0 !!""#

$

%%&

'=

(µ)

( (3.17)

The suppression factor, S is required to account for the fact that nucleation is more

strongly suppressed when the macroscopic convective effect increases in strength and

the wall superheat diminishes. To calculate this suppression factor, Chen used a

regression analysis of the data to fit S as a function of a two phase Reynolds number

defined as:

!

Re tp = Re l F Xtt( )[ ]1.25

(3.18)

37

Chen originally presented the suppression data in graphical format. However, Collier

[45] found the following empirical fit for the suppression factor (which is used in this

study):

( ) ( )117.16Re1056.225.1Re

!!+= tptp xS (3.19)

Collier, also, provided empirical fits for the F(Xtt) data in the form:

!

F Xtt( ) =1 for X

tt

-1 " 0.1

F Xtt( ) = 2.35 0.213+1

Xtt

#

$ %

&

' (

0.736

for Xtt

-1 > 0.1

(3.20)

The Martinelli parameter

!

Xtt is calculated as:

1.05.09.0

1

!!

"

#

$$

%

&!!"

#$$%

&!"

#$%

& '=

g

l

l

g

ttx

xX

µ

µ

(

( (3.21)

Shah Correlation

In the Shah Correlation the heat transfer coefficient takes the form:

( )lel

s FrBoCofh

h,,==! (3.22)

38

With the relevant dimensionless parameters provided as:

5.08.0

1

!!"

#$$%

&!"

#$%

& '=

l

v

x

xCo

(

( (3.23)

lvGh

qBo

"

= (3.24)

gD

GFr

l

le 2

2

!=

(3.25)

The original Shah correlation was presented in graphical form. In 1982 Shah provided

a computational representation of his correlation. This computational representation

was outlined as follows:

04.0Frfor le!=CoN

s (3.26)

04.0Frfor 038.0le

3.0<=

!CoFrN

les (3.27)

4-11EBofor 7.14 !=sF (3.28)

4-11EBofor 4.15 <=sF (3.29)

39

8.08.1

!=

scbN" (3.30)

For Ns > 1

4-0.3E Bofor 2305.0

>= Bonb

! (3.31)

4-0.3E Bofor

4615.0

!

+= Bonb

" (3.32)

( )nbcbs

!!! ,max = (3.33)

For Ns =< 1

( )1 N 0.1for

2.74NexpBo

s

-0.1

s

0.5

!<

=sbsF"

(3.34)

( )1.0 Nfor

2.47NexpBo

s

-0.15

s

0.5

!

=sbsF"

(3.35)

3.2.5 Unresolved issues in two-phase behavior in microgaps

Although there are numerous studies and data on two-phase heat transfer in miniature

and micro channels in the literature, nearly all of these address “ideal” channels, i.e.,

channels that are long enough to produce developed flow and have a uniform heat flux

40

applied along the channel walls. The application of these results and correlations to the

direct cooling of advanced microelectronic chips in non-ideal channels, with non-

uniform heating and relatively short channel lengths, requires dealing with several

unresolved issues.

As discussed in Chapters 1-2, advanced IC’s and especially contemporary

microprocessor architectures experience a high level of transistor modularity that

directly results in non-uniform heating or zonal heating at the die junction (power)

plane. This advancement has resulted in substantial die heating non-uniformity and has

necessitated use of die power (heating) maps to correctly determine the chip

temperature distribution and evaluate the effectiveness of applied thermal management

solutions. . Since the development of the thermal boundary layer in convective heat

transfer and wall ebullition in two-phase flow depend strongly on the local wall heat

flux, it can not be assumed a priori that the available uniform wall heat flux

correlations for the heat transfer coefficients in convection and flow boiling,

respectively, will correctly predict “real” microgap channel behavior. Furthermore, the

focus on miniaturization and compactness in the development of microgap and

microchannel coolers for microelectronic devices results in the design of relatively

short channels with strongly developing flow and significant conductive/convective

conjugate effects in the thermally conductive semi-conductor chips. The available

conventional correlations, with isoflux or isothermal (uniform) boundary conditions

are again inappropriate for predicting the thermofluid behavior of such actual

41

microgap cooler channels. The modeling approached for determining the heat transfer

coefficients prevailing in such channels will be discussed in detail in Chapter 5.

42

Chapter 4:

Experimental Apparatus

4.1 Overall Description

An experiment setup was designed and built for conducting the experimental aspects

of this research. The setup was built around the thermal test chip based on the Intel’s

“Merom” microprocessor [51]. The system was designed to enable flow boiling. An

overall 3-D image of the setup is shown in Figure 14. Schematic layout of the overall

setup is also shown in Figure 15, including the boiling chamber, filling/venting port,

condenser (heat exchanger,) pump, flow meter, inline heater, absolute and differential

pressure transducers and various thermistors including channel (boiling chamber) inlet

and outlet.

43

Figure 14: Two-Phase Microgap Channel Test Apparatus

44

Figure 15: Design Schematics of the Two-Phase Microgap Channel Apparatus

The flow meter is a Kobold Pelton-Wheel Flow meter. It requires a 5V activation

voltage and puts out 4mA to 20mA representing the number of turns that the wheel

makes per second. The flow meter is equipped with an optical sensor that measures

the RPM’s of the wheel.

The Pump is a KAG M42x30/I positive displacement, mag-drive, gear pump. It

supplies up to around 100 psi positive pressures or a maximum of 9 ml/s volumetric

flow rate.

The absolute pressure sensor sends a current range from 4mA to 20mA that linearly

represent pressures from -15 psi to 45 psi or -1 atm to 3 atm. The data acquisition

system can read the current that the pressure sensor puts out.

The test channel cross-pressure transducer is very similar to the absolute Pressure

sensor. The only difference is that it relates a voltage to pressure instead of a current

to pressure. It emits a voltage between 0.05 and 5.05 volts that correspond to a

pressure differential of 0-2 psi (0-13.8 kPa).

The inline heater is used for preheating the fluid coming into the test channel to

whatever desired temperature value. The preheating is done by varying the input

voltage to the heater as the later has a predetermined electrical resistance. The

preheating process is usually required to produce saturated flow boiling at the entrance

of the test channel.

45

The condenser is a flat plate heat exchanger that can be either cooled by natural

convection air or by forced convection water. The later process is usually used in flow

boiling in order to condensate the coolant vapor into liquid before it passes again

through the pump.

Figure 16 shows this process of externally water cooling the condenser and condensing

the working fluid before it flows back to the pump.

Figure 16: External Water-Cooled Condenser for the two-Phase Microgap

Channel Apparatus.

A fluid reservoir, as shown in Figure 17, is used in certain high-pressure tests as a

pressure relief to the system mainly for saturated boiling.

46

Figure 17: Pressure Relief Reservoir for the two-Phase Microgap Channel

Apparatus.

4.2 Calibration of flow meter

The Pelton wheel flow meter measures flow rate by counting the revolutions of a

paddle wheel immersed in the pumped fluid. The number of revolutions per unit time

is translated into a flow measurement. The flow meter outputs an electric current value

that is proportional to the wheel’s RPM. The RPM is converted into flow rate

throughout the measurement process. It is thus imperative to calibrate the flow meter

against the fluid under consideration as fluid properties, including density and

viscosity, influence the flow meter current output. The outcome of the calibration

process is to establish the current vs. flow rate calibration curve that is later

47

programmed into the data acquisition system such that the output by the data file

would be the correct fluid flow rate.

Figure18 shows the flow meter current vs. flow rate calibration curves, extracted via

this method, for water and HFE-7100, respectively.

Figure 18: Kobold Flow Meter Calibration Curves for Water and HFE-7100.

4.3 Chip Thermal Test vehicle

The Thermal Test Vehicle (TTV) is a thermal test chip emulating the Intel Merom

microprocessor. The chip is packaged in a C4 flip chip die mounted via a BGA layer

on an organic substrate. The TTV is depicted in Figure 19.

48

Figure 19: Intel’s Merom Processor Thermal Test Vehicle (TTV) [51].

The TTV is equipped with temperature sensors (Figure 20) that are pre-calibrated

using a four-wire resistance calibration method. Power dissipation on the test chip is

generated by powering, via external power supplies, the three serpentine-type heater

zones (Figure 21) embedded in the chip junction plane.

Figure 20: Intel’s TTV Schematic Three Different Power (Heating) Zones with

Locations of Temperature Sensors.

49

Figure 21: Intel’s TTV Serpentine-Type Heating Zones and Locations of

Temperature Sensors [51].

These three zones, superimposed in Figure 22, at the die area, emulate the half-die and

the two quadrants of the microprocessor. The TTV is enabled to run the heater zones

together to produce uniform power dissipation in the plane pf the resistors or the zones

can be run individually or in binary combinations to produce various non-uniform

power dissipation distributions. The heat flux achievable for uniform power dissipation

is 50 W/cm2 and it can rise to 200 W/cm

2 for non-uniform power dissipation where the

full power is concentrated on one quadrant of the chip area.

50

Figure 22: Assembled Intel TTV Showing Locations of the Three Heater Zones.

The TTV is mounted via a socket connector onto a test board, as shown in Figure 23,

that provides the connection necessary to power the TTV chip and read the resistors

from the temperature sensors and convert them into temperature values through the

data acquisition system.

51

Figure 23: Intel’s TTV Board.

4.4 The microgap test channel

An hermetically sealed fluid chamber is assembled on the TTV die to allow the

coolant to flow in direct contact with the silicon die. The chamber is constructed with

a copper base that is attached to the TTV board via an O-ring. The copper channel

(shown in Figures 24, 25) is covered at the top by a plastic cap and attached via a

second O-ring. The fluid height in the channel, i.e., the fluid gap, is determined by

sandwiched plastic inserts that have variable thicknesses to produce the desired fluid

gap, as shown in Figure 25.

52

Figure 24: TTV Cooper Channel

Figure 25: Hermetically Sealed Microgap Channel.

53

4.5 Chip TTV - Sensor Calibration Procedure

The sensor calibration process is a necessary step in converting the sensor resistances

to the actual temperatures. This process, i.e., four-wire resistance calibration, involves

placing the TTV in a constant temperature bath, soaking the unit for a sufficient

amount of time to establish l thermal equilibrium and measuring the resistance of the

temperature sensor along with the temperature of the fluid bath. This step is repeated at

four different fluid bath temperatures. Finally, a linear regression is performed to

establish the resistance vs. temperature calibration curve. Figure 26, shows a typical

sensor calibration curve for the four-wire measurement process.

Figure 26: TTV Characteristic Temperature Sensor Calibration.

54

4.6 Fluid selection and HFE-7100 Novec properties

Water’s thermal characteristics including thermal conductivity, specific heat and latent

heat of vaporization, make it an ideal and the most popular coolant for a wide variety

of thermal management applications. However, water is electrically conductive and

could cause device failure and IC shorting, as well as corrosive actions, if a water-

cooled thermal management component experiences leakage. The industry, therefore,

prefers dielectric fluids for advanced liquid cooling of electronic components.

Historically, the dielectric fluorinerts [52], i.e., the FC family of fluids, along with

other refrigerants (such as R134x, etc.) had been extensively used in liquid cooled

products. These fluids, however, do not possess good environmental properties,

displaying high global warming potential (GWP) and ozone depletion potential (ODP)

[52]. The chemical industry led by 3M pioneered a new family of liquid cooling

products, Novec, aimed at addressing the environmental and toxicity aspects and

characteristics of FC’s. 3M™ Novec™ 7100 Engineered Fluid [52], is used in the

present work. HFE-7100, chemically known as methoxy-nonafluorobutane

(C4F9OCH3), is a clear, colorless and low-odor fluid intended to replace ozone-

depleting substances (ODSs) and compounds with high global warming potential

(GWP). This proprietary fluid has zero ozone depletion potential and other favorable

environmental properties (see Table 1). It has one of the best toxicological profiles

(Table 2) of CFC replacement materials, with a time-weighted average exposure

guideline of 750 ppm (eight hour average). Table 3, shows published properties from

55

3M on both FC and Novec family of fluids.

The boiling point and low surface tension of Novec HFE-7100 fluid as well as its

chemical and thermal stability, non-flammability and low toxicity make it ideal for use

in liquid cooling industrial applications. Table 4, shows the thermal and fluid

properties of HFE-7100 compared to water and other refrigerants used for liquid

cooling. Figure 27, shows the HFE-7100 temperature-dependent properties used in the

present work.

Table 1: HFE-7100 Environmental Properties [52].

56

Table 2: HFE-7100 Toxicity Properties [52].

57

Table 3: Characteristics of 3M’s Fluorinert and Novec Fluids [52].

Property HFE-7100 FC-72 R-134a R-245a Water

Chemical Formula C4F9OCH3 C6F14 C2H2F4 CHF2CH2CF3 H2O

Boiling Point (1atm) [°C] 61 56 -26 14.9 100

Density [kg/m3] 1510 1680 1377 1366 1000

Surface Tension [dyne/cm] 12.3 12 15.3 - 58.9

Kinematic Viscosity [cSt] 0.38 0.38 2.74 3.43 2.87

Latent Heat of Vaporization [kJ/kg] 121.2 88 212.1 197.3 2257

58

Specific Heat [kJ/kg.K] 1.25 1.1 1.28 1.31 4.08

Thermal Conductivity [W/m.K] 0.062 0.057 0.105 0.084 0.681

Dielectric Strength [kV/mm] 11 15 7 - -

Dielectric Constant 7.4 1.76 9.5 - 78.5

Table 4: HFE-7100 Thermo-Physical Properties Compared to Other Coolants.

Figure 27: HFE-7100 Thermal and Fluid Properties [52].

59

Chapter 5:

CFD Model and Simulation

5.1 Introduction

Thermal issues have become a major concern in electronics design reflecting the effect

of increasing power densities, demands on reliability, and die junction temperature

limits. The industry, therefore, has seen an increased focus on the thermal performance

of packaging materials, cooling devices, and design and analysis tools. This focus has

resulted in the commercial availability of advanced Computational Fluid Dynamics

(CFD) tools to solve the simultaneous equations of fluid dynamics and heat transfer or

the so-called conjugate heat transfer problem. These tools are based on the finite

element, finite difference, or control volume numerical methods to analyze three-

dimensional geometries by solving steady state as well as transient governing

equations. In the present work, the commercially available CFD package Icepak [53]

from Ansys, was used for the modeling of the test microgap cooling channel and

solving the fully conjugate heat transfer-fluid problem.

5.2 Equations Solved and Methodology

The governing equations solved in this CFD simulation are the Navies Stokes partial

differential equations for the conservation of momentum, along with equations for the

60

conservation of mass (continuity) and conservation of energy. The three equations take

the following forms

!

" #r u = 0 (5.1)

!

"#r u

#t+ "(

r u $ %)

r u = &%P + "%2

r u + "

r g '(T &T() (5.2)

!

"cp

#T

#t+ "c p

r u $ %T =% $ k%T + S (5.3)

The conjugate flow and heat solution is obtained using the Boussinesq approximation

for buoyancy forces.

!

"g(# " #amb ) = #ambg$(T "T%) (5.4)

Thermal radiation is a non-linear phenomenon and solved for fully by calculating

exchange factors for all surfaces and adding an appropriate term to the energy equation.

!

Q ="#AT 4 (5.5)

61

The real physical geometry is discretized (Figure 28) into small volumes known as

grid cells. The above equations are applied on each cell and implemented as algebraic

equations while temperature, pressure and x, y and z fluid velocities are assumed

constants for each cell. The algebraic equations are solved for the entire computational

domain (the computational grid) iteratively until an acceptable converged solution is

found [54].

Figure 28: The CFD Computational Grid.

5.3 Model Description and conjugate heat transfer

A Computational Fluid Dynamics (CFD) model was created for the test channel

including the entire fluid chamber, silicon die test chip, printed circuit test board and

inlet and outlet pipes. The simulation used a fully conjugate heat transfer model, i.e., it

solved for heat transfer internal to the channel and external to it involving automatic

calculation of convective and radiative hear transfer with both the working fluid and

62

the ambient room air. A grid sensitivity analysis was conducted to reach a solution

that is grid-independent. The computational grid is shown in Figures 29 and 30 for a

close-up on the fluid channel and the entire conjugate domain, respectively.

Convergence of temperature results for the key chip temperature sensors are shown in

Figure 31. The model computational domain reached a grid that is 1.3 million

computational cells. Figures 32 and 33 show detailed three-dimensional, XY and YZ

views of the computational domain, respectively.

Figure 29: Fluid Channel Grid.

63

Figure 30: Full Conjugate Domain Grid.

Figure 31: CFD Solution Convergence for Key Temperature Sensors.

64

Figure 32: 3-D View of the Microgap Fluid Channel CFD Model.

65

Figure 33: XY and YZ Views of the Microgap Fluid Channel CFD Model.

Note that the domain contains a sufficiently large volume of the surrounding ambient

in the calculation such that the radiative and convective heat transfer between the

chamber and the surrounding air are automatically calculated by the software and not

prescribed or approximated. This makes it possible to precisely determine the heat

losses from the test vehicle and to then assess - in all run cases - the fraction of power

going into the coolant fluid inside the channels, i.e., the “conversion” rate. The die

junction plane (where the power is dissipated) was modeled identically to represent the

actual serpentine-like junction plane (Figure 21) in the actual thermal test chip. The

half die and two quadrants are easily identified in Figure 34. This enables running

uniform and non-uniform power dissipation in the numerical thermal-CFD model.

66

Figure 34: Model of the Junction Plane Showing the Emulated Serpentine-Type

Heating Zones.

67

Chapter 6:

Single-Phase Data and Discussion

6.1 Basic relations

The thermal performance of a micro gap (micro channel) is characterized by the

dimensionless Nusslet number (Nu) as given by

!

Nu =hD

h

k (6.1)

Where

!

k is the fluid thermal conductivity,

!

Dh is the gap hydraulic diameter as given

by

!

Dh =4.(cross sec tion area)

wetted perimeter (6.2)

and

!

h is the micro gap heat transfer coefficient. The heat transfer coefficient is given

by

!

h =q

A"T (6.3)

68

Where,

!

"T is the temperature difference between the heated surface (die average

temperature) and the fluid average inlet temperature,

!

q is the heat transfer rate to the

fluid (heat dissipated into fluid from the die surface) and

!

A is the heated wall surface

area. The heat transfer rate can be determined from an energy balance on the channel

via the equation

!

q = m•

Cp (Toutlet "Tinlet ) (6.4)

Where

!

m

•

is the fluid mass flow rate while

!

Toutlet

and

!

Tinlet

are the channel fluid outlet

and inlet temperatures, respectively.

From the above equations, the heat transfer coefficient and Nusslet number can be

calculated by the following expressions,

!

h =m•


A#T (6.5)

!

Nu =m•


A#T

Dh

k (6.6)

6.2 Error Analysis

69

The test measurement error can be divided into bias errors and precision errors [54].

The bias error remains constant during the measurements under a fixed operating

condition. The bias error can be estimated by calibration, concomitant methodology,

inter-laboratory comparison and experience. When measurements are repeated under

fixed operating conditions, the precision error is affected by the repeatability and

resolution of the equipment used, the temporal and spatial variation of variables, the

variations in measured variables, and variations in operating and environmental

conditions in the measurement processes. Each measurement error would be combined

with other errors in some manner, which increases the uncertainty of the measurement.

A first-order estimate of the uncertainty in the measurement due to the individual

errors can be computed by the root-sum-square method [55].

The uncertainty in the single-phase heat transfer coefficient, obtained from the channel

energy balance equation above, is linear and is affected by the uncertainties in the

measured quantities including the flow rate, the temperature of the wall (die sensors),

the temperature of inlet and outlet, the stability of the data logger and power supply. It

can be expressed mathematically as

!

"h

h

#

$ %

&

' (

2

="m

•

m•

#

$

% %

&

'

( (

2

+"q

q

#

$ %

&

' (

2

+")Twall)Twall

#

$ %

&

' (

2

(6.7)

70

Where

!

" h is the uncertainty of the heat transfer coefficient,

!

"m•

is the error of flow

rate via the flow meter,

!

"q is error of input power via the power supply,

!

"#Twall

is the

measurement error of wall excess temperature. The flow meter’s flow rate error is ±

1.5%. The error of the power supply is ± 2.5%. The maximum error in the wall excess

temperature measurement is ± 0.25°C which causes maximum error of 1%. Thus, the

possible maximum error in measuring the heat transfer coefficient is ±3%.

The uncertainty in the measured pressure drop across the gap (channel) is determined

by the accuracy of the pressure transducer (± 0.25% Full Scale). However, uncertainty

of the measured pressure drop is linearly dependent on the uncertainty in the

measurement of flow. Therefore the resulting uncertainty of measuring pressure drop

can be expressed as

!

"#P

#P

$

% &

'

( )

2

="m

•

m

•

$

%

& &

'

(

) )

2

+"#P

t

#Pt

$

% &

'

( )

2

(6.8)

Where

!

"P is pressure drop and

!

"#P is the uncertainty of pressure drop measurement

and

!

"#Pt is the error of the pressure transducer. The error of pressure transducer is ±

0.25% FS. Therefore, the possible maximum error in the pressure drop measurement is

1.52%.

71

It should be noted that the above error analyses for both pressure drop and heat transfer

coefficient measurements do not include the uncertainty and variation of HFE-7100

fluid properties, as there is no data (up to the author’s knowledge) on the uncertainty

of this fluid’s properties in the literature.

6.3 Single Phase Results

6.3.1 Comparison of Experimental, CFD and Theoretical Correlations

To initiate operation of the test facility and validate the measurement procedures in

preparation for the two-phase experiments, single phase hydrodynamic and heat

transfer characteristics of the 100-micron channel, with HFE-7100 coolant, were

studied. CFD model runs are compared to actual tests for various flow rates (1-9 ml/s),

which correspond to an average velocity range of 0.7-6.5 m/s, and the results are

depicted in Figures 35-36. Figure 35 shows the hydrodynamic performance

comparisons i.e., pressure drop (!P) in the channel while Figure 36 shows the channel

average heat transfer coefficient (h) comparisons. The figures also show the error

(uncertainty) bar associated with testing data. Good accuracy is established from the

CFD model as most of the pressure drop test results fall within 10% of the anticipated

!P uncertainty error bar, while the heat transfer coefficient errors fall within 4% of the

associated h uncertainty error bar. The measurement errors are larger than the

predicted uncertainty and this is largely due to the uncertainty and variation of HFE-

7100 fluid properties. M.S. El-Genk [56] studied pool boiling using HFE-7100 and

72

reported correlations errors of 10% larger than the measurement uncertainty of 3.7%.

Similar fluid-properties based errors were reported by Kim et al, [19].

Figure 35: Effect of Fluid Velocity on Single-Phase Pressure Drop in a 100-

micron Microgap Channel Flowing HFE-7100 (Dh = 200 micron).

73

Figure 36: Effect of Fluid Velocity on Single-Phase Heat Transfer Coefficient in a

100-micron Microgap Channel Flowing HFE-7100 (Dh = 200 micron). P=10W,

Tin=23C.

The single-phase hydrodynamic (pressure drop) and thermal (heat transfer coefficient)

correlations discussed in Chapter 2, relate to an ideal channel of ideal boundary

conditions, i.e., ideal channel geometries with the characteristics of the uniform flow,

laminar-developing flow, uniform wall (planar) heating and negligible conjugate heat

transfer effects. Figure 37 depicts the pressure drop as a function of velocity using the

ideal channel correlation (in Chapter 2) and the corresponding actual test channel

measurements and the CFD model results superimposed across the velocity range

considered. Note, that the range of Reynolds number (Re) experienced was 380-3500

for the velocity range considered (0.7-6.5 m/s) where all the data was in the laminar

74

flow regime except for the last two data points (at 5 m/s and 6.5 m/s velocities or Re of

2700 and 3500, respectively) where the flow was in the laminar-to-turbulent transition

regime. On the other hand, due to the very short channel considered (10.5 mm in

length), the hydrodynamic entry length - approximately given by

!

0.05.Re.Dh [25] -

was higher than the channel length across the velocity range considered, except for the

very low velocities of 0.7 m/s and 1.5 m/s, for which, the channel experienced a

combination of developing and fully developed flow. The thermal entry length given

by

!

0.05.Re.PrDh [25] was, however, higher than the channel length across the full

velocity range considered and thus the thermal transport in the channel was always in

the developing flow condition.

While CFD results do not agree well with the correlations, they however can simulate

these non-idealities and show good agreement with actual measurements. Using the

ideal channel correlation to predict the actual non-ideal channel measured pressure

drops, provides a similar trend with fluid velocity but yields an average error of 24%

with the largest error at the low velocities. The CFD model, however, provides much

better agreement with measurements whereby the average error is reduced to 5%.

Figure 38 depicts the heat transfer coefficient as a function of flow rate using the ideal

channel correlation and the corresponding actual test channel measured heat transfer

coefficient’s, superimposed across the velocity range considered. Very similar

conclusions, to those of the hydrodynamic ones, can be drawn for the heat transfer

75

results. The average error of using the ideal geometry channel heat transfer coefficient

correlation to predict the actual complex channel heat transfer coefficient is 7% and

the error is largest at the low velocities. The CFD model provides better agreement

with measurements whereby the average error is reduced to 4%.

These findings help make two main points; establishing credibility and accuracy of the

CFD model of the non-ideal (actual complex geometry) channel and determining the

error margin associated with single-phase correlation. The later finding will be very

important in the later analysis of two-phase correlation accuracy in later chapters.

Figure 37: Single-Phase Pressure Drop vs. Velocity for HFE-7100 in a 100-micron

Microgap Channel (Dh=200 micron).

76

Figure 38: Single-Phase Heat Transfer Coefficient vs. Velocity for HFE-7100 in a

100-micron Microgap Channel (Dh=200 micron). P=10W, Tin=23C.

6.3.2 Raw temperature data and Comparison to CFD

The measured temperatures obtained from the sensors embedded in the die surface

(wall), due to the nearly-uniform heating across the entire junction plane of die and

with HFE-7100 flowing and with 1ml/s and 9 ml/s, respectively, is shown in Table 5.

The 1 ml/s and 9 ml/s flow rates correspond to Reynolds numbers of Re=380 and

Re=3420, and to velocities of 0.7 m/s and 6.5 m/s, respectively. CFD model results are

shown along with the test data. The percentage errors, relative to fluid inlet

temperature Tin=23C, were calculated and tabulated as well. Good agreement is

77

established between test and CFD model results as shown in Table 5 with respect to

individual sensor temperatures and wall average, minimum and maximum

temperatures with maximum error at ~ 5%.

Table 5: Sensor Temperatures for the Uniformly Heated 100-micron Microgap

Channel with the Flow of HFE-7100, Tin=23°C, q!=7W/cm2.

The measured temperatures obtained from the sensors embedded in the die surface

(wall), due to the half-die and quadrant-die non-uniform heating across the entire

junction plane of die and with HFE-7100 flowing and with 1ml/s and 9 ml/s,

respectively, are shown in Tables 6 and 7. CFD model results are shown along the test

data. The percentage errors, relative to fluid inlet temperature Tin=23C, were

calculated and tabulated as well. As with the uniform heating case above, good

agreement is established between testing and CFD model data as shown in Tables 6

78

and 7 with respect to individual sensor temperatures and wall average, minimum and

maximum temperatures with maximum error at ~ 10%.

Table 6: Sensor Temperatures for the Half-Die Heated 100-micron Microgap

Channel with the Flow of HFE-7100, Tin=23°C, q!=7W/cm2.

Table 7: Sensor Temperatures for the Quadrant-Die Heated 100-micron

Microgap Channel with the Flow of HFE-7100, Tin=23°C, q!=7W/cm2.

79

The die surface (wall) sensor average excess temperature (temperature rise above the

23C inlet) is shown in Figure 39 for the test and CFD model results for 100-micron

channel and uniform heating across a range of 1-9 ml/s flow rates (0.7 to 6.5 ml/s

velocity). It is worth mentioning that the discrepancy in sensor excess temperature

between experimental and CFD simulation results are 2% and 4%, respectively.

Figure 39: Die Average Sensor Excess Temperature Test Data and CFD

Simulation vs. Velocity, HFE-7100 flowing in a 100-micron Microgap Channel

and Uniform Heating q!=7W/cm2.

The accuracy of die sensor temperatures, embedded at the junction plane, compared to

the actual wall temperatures (the surface plane), is performed. Tables 8, 9 and 10 show

the nine sensor temperatures (101-109) along with their average, minimum and

80

maximum values at both the junction plane and at the wall (surface plane) for variable

flow rates (1-9 ml/s). The sensor average, minimum and maximum temperatures are

shown to be close to their footprint locations at the surface (wall) plane with a

maximum difference percentage of <2%. While the temperatures at the junction plane

are not very different from their footprints at the surface plane, better results can be

obtained by using the CFD-derived surface temperatures and this will become more

important at the higher heat fluxes of two-phase flow.

Flow rate

(ml/s) 1 2 3 5 7 9

101 44.86 40.86 37.90 34.48 32.41 30.93

102 45.81 41.64 38.58 35.05 32.96 31.44

103 44.66 40.90 37.91 34.55 32.44 30.95

104 45.66 41.66 38.63 35.16 33.05 31.53

105 43.24 39.03 36.10 32.73 30.74 29.33

106 41.67 38.07 35.32 32.21 30.24 28.90

107 45.48 41.49 38.46 34.99 32.89 31.38

108 43.59 39.37 36.43 33.03 31.01 29.58

109 42.07 38.44 35.68 32.54 30.54 29.17

Average 44.12 40.16 37.22 33.86 31.81 30.36

Surface Average 44.55 40.57 37.57 34.13 32.04 30.54

Difference Percentage

(%) 1 1 0.9 0.8 0.7 0.6

Minimum 41.67 38.07 35.32 32.21 30.24 28.90

Surface Minimum 41.57 37.89 35.11 31.94 29.94 28.59

Difference Percentage(%) -0.2 -0.5 -0.6 -0.8 -1 -1.1

Maximum 45.81 41.66 38.63 35.16 33.05 31.53

Surface Maximum 45.95 41.82 38.71 35.15 33 31.44

Difference Percentage(%) 0.3 0.4 0.2 0 -0.2 -0.3

81


Temperatures for 100-micron Channel and Uniform Heating with the flow of

HFE-7100, Tin=23°C, q!=7W/cm2.

Flow rate

(ml/s) 1 2 3 5 7 9

101 52.60 48.18 44.76 40.72 38.14 36.21

102 40.89 36.96 34.12 30.94 29.13 27.85

103 39.92 36.36 33.58 30.56 28.73 27.50

104 52.05 47.76 44.40 40.47 37.99 36.13

105 37.26 33.53 31.00 28.25 26.75 25.76

106 36.09 32.86 30.48 27.94 26.46 25.53

107 39.81 36.09 33.32 30.27 28.51 27.29

108 50.05 45.33 41.95 37.92 35.40 33.54

109 48.20 44.19 41.02 37.29 34.78 32.99

Average 44.09 40.14 37.18 33.82 31.77 30.31

Surface Average 44.51 40.53 37.52 34.09 32 30.51


(%) 0.9 1 0.9 0.8 0.7 0.6

Minimum 36.09 32.86 30.48 27.94 26.46 25.53

Surface Minimum 35.97 32.7 30.31 27.76 26.29 25.37

Difference Percentage(%) -0.3 -0.5 -0.6 -0.6 -0.7 -0.6

Maximum 52.60 48.18 44.76 40.72 38.14 36.21

Surface Maximum 52.59 48.05 44.6 40.51 37.95 36.01

Difference Percentage(%) 0 -0.3 -0.4 -0.5 -0.5 -0.6


Temperatures for 100-micron Channel and Half-Die Heating with the flow of

HFE-7100, Tin=23°C, q!=7W/cm2.

82

Flow Rate (ml/s) 1 2 3 5 7 9

101 37.87 34.36 31.81 28.97 27.37 26.29

102 55.34 51.00 47.62 43.53 40.97 39.01

103 43.02 39.36 36.40 33.02 30.94 29.47

104 39.82 36.21 33.51 30.46 28.70 27.48

105 54.54 49.75 46.18 41.78 38.91 36.76

106 39.98 36.46 33.73 30.62 28.70 27.40

107 50.10 46.06 42.84 39.03 36.65 34.87

108 38.66 34.90 32.29 29.34 27.68 26.55

109 35.60 32.48 30.19 27.69 26.26 25.36

Average 43.88 40.07 37.17 33.83 31.80 30.35

Surface Average 44.31 40.47 37.51 34.09 32.02 30.53


(%) 1 1 0.9 0.8 0.7 0.6

Minimum 35.60 32.48 30.19 27.69 26.26 25.36

Surface Minimum 35.47 32.32 30.01 27.51 26.1 25.2

Difference Percentage(%) -0.4 -0.5 -0.6 -0.6 -0.6 -0.6

Maximum 55.34 51.00 47.62 43.53 40.97 39.01

Surface Maximum 56.44 51.75 48.18 43.82 41.04 38.9

Difference Percentage(%) 1.9 1.5 1.2 0.7 0.2 -0.3


Temperatures for 100-micron Channel and Quadrant-Die Heating with the flow

of HFE-7100, Tin=23°C, q!=7W/cm2.

6.3.3 Conjugate effects and conduction spreading in advanced microprocessors

The theoretical relations and empirical correlations for single phase heat transfer

available in the literature neglect the impact of conjugate heat transfer associated with

conduction spreading within the thermally conductive blocks of semiconductor die

83

chips. These theoretical formulations are based on uniform heat flux or uniform

temperature boundary conditions on the surface interacting with the cooling fluid.

Similarly, researchers in the field, when conducting single-phase heat transfer

experiments, strive to produce either a fixed flux or fixed temperature wetted surface.

Thus, nearly all the available formulations for predicting the convective heat transfer

coefficient are based on these ideal boundary conditions. Due to the generally non-

uniform heating in an operating chip, and despite the high thermal conductivity of

silicon, conjugate effects must be included in any effort to achieve a precise

temperature prediction for a convectively cooled chip. Consequently, in the current

study, a detailed thermofluid numerical model of the test apparatus and the heated chip

was created and validated by a comparison of the predicted temperatures at the

locations of nine distinct sensors embedded in the “junction” plane of the chip.

The importance of resolving the spatial distribution of heat flux (the heat flux map) at

the wall surface and resultant distribution of the surface heat transfer coefficients for

the 800-micron thick chip with an average conductivity of 120 W/mK, can not be

overstated. Figures 40, 41 and 42 below, graphically illustrate this conduction

spreading effect on the three heating patterns studied, i.e., uniform heating, half die

heating and quadrant die heating, respectively.

84

Figure 40: Conduction Spreading Conjugate Effect on Wall Spatial Heat Flux

and Heat Transfer Coefficient for Uniformly Heated 100-micron Channel with

the Flow of HFE-7100, Tin=23°C, q!=7W/cm2.

85


and Heat Transfer Coefficient for Half-Die Heated 100-micron Channel with the

Flow of HFE-7100, Tin=23°C, q!=7W/cm2.

86


and Heat Transfer Coefficient for Quadrant-Die Heated 100-micron Channel

with the Flow of HFE-7100, Tin=23°C, q!=7W/cm2.

Figures 40-42 show the spatial heat flux distribution and spatial temperature

distribution on three different planes that slice through the silicon chip: at the junction

plane (where the heat is applied,) at mid plane and at the top die surface (wetted wall).

87

The figures reference the results three different heating patterns of the 100-micron

channel flowing HFE-7100 with Tin=23°C and q!=7W/cm2.

While the spatial temperature plots do not change much in pattern, it is clear that the

heat flux distribution on the wetted surface changes dramatically across the thickness

of the silicon die from the junction (bottom) plane to the top surface.

Most importantly, it is found that while the silicon conduction spreading does smooth

out the serpentine pattern applied to the full junction plane of the chip, it does not yield

a uniform heat flux wetted surface. Rather, the combined conduction-convection

effects on this chip with an average heat flux of 6.5W/cm2 result in highly non-uniform

heat flux at the wetted wall, with a peak heat flux reaching 10W/cm2 at the axial

centerline near the inlet to the microgap channel and steep axial and lateral gradients

that yield a flux of 2.5W/cm2 at the channel outlet along the centerline and 4W/cm

2 at

the lateral edges. This highly non-isoflux condition, combined with the non-isothermal

condition, lead to a complex temperature-flux distribution on the wetted surface and

clearly explains why available uniform heat flux correlations failed to predict

accurately the spatial wall heat transfer coefficient.

As with uniform heating, non-uniform heating represented by the half-die heating and

quadrant-die heating shown in Figures 41 and 42, the conjugate effect (die silicon

block conduction spreading) has a similar effect in changing the resultant surface heat

flux and heat transfer coefficient. However, due to the concentrated heat and thus heat

flux at the junction plane with these non-uniform heating types, the resultant surface

88

heat fluxes have a somewhat similar distribution to those at the junction plane. This is

clearly shown in Figures 41 and 42 where the highest heat flux is seen at the same

locations as in the junction plane, i.e., left half of the die with half-die heating and

bottom left quarter of the die with quadrant-die heating.

The availability of the full CFD model makes it possible to refine the calculation of the

heat lost from the junction plane to the larger package and housing of the test chamber.

Consequently, for the evaluation of the efficacy of the apparatus and for determination

of the average heat transfer coefficient, a conjugate thermal analysis was performed to

determine the percentage of heat going into the channel fluid, i.e., the heat conversion

rate versus the heat conducted into the chip substrate and the surrounding structure.

The conversion rate was used in the calculations of the average heat transfer

coefficients shown in Figures 36 and 38. The resulting conversion rates are shown in

Figure 43 for the fluid inlet velocity range considered. It is clearly shown, that the

conversion rate, i.e., heat dissipated across the wetted surface and into the flowing

liquid, increases with the fluid inlet velocity, rising from 7.6W to 9.4W of total chip

power (10W) as the fluid inlet velocity increases from 0.7 m/s to 6.5m/s.

89

Figure 43: Single-Phase Conjugate Heat Transfer Conversion Rate vs. Fluid Inlet

Velocity for the 100-micron Microgap Channel. P=10W, Tin=23C.

6.3.4 Temperature Distribution – Uniform Heating

The temperature distribution, obtained from the validated CFD model, at the die

surface (wall), due to the nearly-uniform heating across the entire junction plane of the

die and with HFE-7100 flowing at velocities of 0.7 m/s and 6.5 m/s (1ml/s and 9 ml/s),

respectively, is plotted in Figure 44. It is clearly observed, that due to the non-ideal

characteristic of the channel, including developing flow heat transfer coefficients and

conduction in the silicon chip, as well as the sensible temperature rise in the coolant

and despite the nearly-uniform heating in the die junction plane, the temperature

distribution is decidedly non-uniform, with a clear main temperature gradient along the

axial (flow) direction and a minor temperature variation along the lateral axis. The

90

temperature profile, with lateral and axial variations of nearly 4.5C, appears to display

an almost axisymmetric distribution with the peak temperature located near the

centerline of the channel but shifted somewhat downstream from the middle of the die.

Velocity Field:

The fluid flow velocity vectors for 0.7m/s and 6.5m/s, respectively, obtained from the

CFD simulation of the microgap channel, are shown in Figure 45, for a plane cutting

across the mid-height of the microgap channel. For the lower velocity, the fluid is seen

to enter the channel at a nominal velocity of 0.7m/s through the inlet, and to diverge

into the channel, impinging on the wetted surface of the die with an oblique – rather

than a purely axial velocity of 0.4 m/s. After washing across the surface of the chip,

the fluid converges towards the outlet and then exits the test chamber. Interestingly it

is seen that some fluid bypasses the center of the chip and flows along the sidewalls

through the 0.5 mm gap between the chip and the left and right sidewalls, respectively.

This produces variation of fluid velocity across the channel width as the velocity

decreases about three folds from the center toward the left and right sides. In an actual

chip package, this gap serves as a “keep-out” zone to protect the chip against possible

mechanical damage (scratches) and/or electrical shorting but this essential feature of

an actual package prevents the fluid from distributing uniformly across the heated

surface. The velocity field for the higher 9m/s velocity displays many of the same

characteristics as the low velocity configuration but the higher momentum associated

with the 6.5m/s inlet velocity results in a jet-like flow down the axial centerline of the

91

chip, with velocities approaching 5m/s, which is dissipated in the broader flow field

well before the outlet.

Pressure Fields:

The pressure distributions through and across the microgap channel are shown in

Figure 46 for the two noted velocities, 0.7m/s and 6.5m/s, respectively. Despite the

small non-uniformity in the velocity profile across the chip, the pressure distribution is

nearly laterally uniform and only varies modestly in the axial direction in the microgap

channel itself. Most of the inlet-to-outlet pressure drop, i.e., 2.6kPa for the 0.7m/s and

77kPa for the 6.5m/s fluid velocities, respectively, occurs in the inlet and outlet zones

due to the divergence and convergence of the flow. In addition, the flow through two,

ninety-degree angles at inlet and outlet, can introduce a significant manifold pressure

drop.

(a) 0.7 m/s (b) 6.5 m/s

92

Figure 44: Chip Surface (Wall) Temperature Distribution of Uniformly Heated

100-micron Microgap Channel - (a) 0.7m/s (left), (b) 6.5m/s (right), Tin =23C.

(a) 0.7 m/s (b) 6.5 m/s

Figure 45: Mid-Height Fluid Velocity Vectors Distribution for a 100-micron

Uniformly Heated Microgap Channel - (a) 0.7m/s (left), (b) 6.5m/s (right).

93

(a) 0.7 m/s (b) 6.5 m/s

Figure 46: Mid-Height Pressure Distribution for a 100-micron Uniformly Heated

Microgap Channel - (a) 0.7m/s (left), (b) 6.5m/s (right).

6.3.5 Temperature Distribution – Half-Die and Quadrant-Die Heating

The temperature distribution obtained from the simulations performed with the

validated CFD model at the channel wall, due to the non-uniform heating of the die, is

plotted in Figures 47 and 48, for the half-die heating and quadrant-die heating,

respectively, and a fluid inlet temperature of 23°C. It is clearly shown that the

temperature distribution is highly non-uniform. The maximum wall temperature is

located around the middle of the heated half-die and heated quadrant-die for both non-

uniform heating cases, respectively. Larger temperature gradient across the die wall is

seen with the non-uniformity cases compared to the earlier uniformly heated case. A

temperature gradient of 16C is seen with the half-die heated channel and inlet fluid

94

velocity of 0.7 m/s with a maximum temperature of 52.6C and a minimum temperature

of 36C. The die wall gradient increases with the quadrant die heating to 20C with a

maximum temperature of 56.4C and a minimum temperature of 35.5C.

(a) 0.7 m/s (b) 6.5 m/s

Figure 47: Chip Surface (Wall) Temperature Distribution of Half-Die Heated

100-micron Microgap Channel - (a) 0.7m/s (left), (b) 6.5m/s (right), Tin=23C.

(a) 0.7 m/s (b) 6.5 m/s

95

Figure 48: Chip Surface (Wall) Temperature Distribution of Quadrant-Die

Heated 100-micron Microgap Channel - (a) 0.7m/s (left), (b) 6.5m/s (right),

Tin=23C.

6.3.6 Inversely Determined Heat Transfer Coefficients

The availability of the detailed thermo-fluid model of the resistance-heated chip

developed in this study also makes it possible to determine the local heat transfer

coefficient, on a cell-by-cell basis, across the die surface based on knowing the cell

temperature and heat flux and the reference temperature, which was assigned to be the

inlet fluid temperature. Applying Newton’s law of cooling on a cell-by-cell basis, the

spatial variations of the heat transfer coefficient across the die surface are shown in

Figure 49 for 0.7m/s and 6.5m/s inlet fluid velocities, respectively. The heat transfer

coefficient distribution for the 0.7m/s inlet fluid velocity, with Re of 380 is nearly

uniform in the lateral direction but varies by a factor of nearly 3.5 in the axial direction,

from a high of 2600 W/m2K at the upstream edge of the chip to 937 W/m

2K at the

downstream edge of the chip. The heat transfer coefficient distribution for the 6.5 m/s

inlet fluid velocity case, with Re of 3420, is highly non-uniform laterally and axially,

varying from a high of 10200 W/m2K at the upstream edge of the chip to 4223 W/m

2K

at the downstream edge of the chip. The higher values of the heat transfer coefficient

and its variation are largely due to the higher fluid velocity associated with the higher

flow rate and the enhanced velocities, previously seen in Fig 41, at the center and sides

of the silicon chip near the liquid inlet to the microgap channel.

96

(a) 0.7 m/s (b) 6.5 m/s

Figure 49: Spatial Variation of Heat Transfer Coefficient for Uniformly Heated


The spatial (local) variations of heat transfer coefficient across the die surface for the

half-die and quadrant-die non-uniform heating are shown in Figure 50 and 51,

respectively. The slight difference of the heat transfer coefficient variations for these

non-uniform heating cases is due to the higher non-uniformity and the skewed

symmetry toward the higher heat flux zones of the chip compared to those of the

uniform heating cases. Similar variation in the axial direction across the chip is seen in

all cases due to the flow velocity profiles as noted earlier. It appears that the flow field

dominates the behavior of the heat transfer coefficient and that due to conduction

spreading in the chip the differences in the thermal boundary condition are minimized

and have only a weak effect on the heat transfer coefficient distribution.

97

(a) 0.7 m/s (b) 6.5 m/s

Figure 50: Spatial Variation of Heat Transfer Coefficient for Half-Die Heated


(a) 0.7 m/s (b) 6.5 m/s

Figure 51: Spatial Variation of Heat Transfer Coefficient for Quadrant-Die

Heated 100-micron Microgap Channel - (a) 0.7m/s (left), (b) 6.5m/s (right),

Tin=23C.

98

6.4 Overall single-phase hydraulic and thermal performance

The overall hydraulic (pressure drop) and thermal performance (heat transfer

coefficient) of the micro gap cooler can be characterized as a function of flow rate,

represented by the corresponding channel Reynolds number (Re,) for the various

channel heights considered in this study, i.e., 100, 200 and 500-micron channels. The

single-phase pressure drop and heat transfer coefficients obtained in this part of the

study are shown in Figures 52 and 53, respectively. It is interesting to note that the Re

is a linear function of the channel mass flow rate (or velocity) as the velocity-hydraulic

diameter product (v.Dh) in Re equation is constant and equal to twice the velocity of

the channel.

It is quite clear, and as expected, that the pressure drop increases with the Reynolds

number in a nearly quadratic fashion, but this dependence is affected somewhat by the

transition from laminar to turbulent flow at a Re of approximately 2300. Moreover, the

pressure drop is also inversely proportional to the channel height for a fixed Re

number (fixed velocity) and follows a second-degree polynomial as per the literature

[26]. For a fixed velocity of 6.5 m/s the pressure drop increases from around 20,000 Pa

for the 500-micron channel to 80,000 Pa for the 100-micron channel.

The heat transfer coefficient is also inversely proportional to the channel height for a

fixed Re number (fixed flow rate.) The heat transfer coefficient varies as a pseudo

linear function of Re number, for values that span the range from laminar flow (at the

99

low flow rates) to turbulent (at high velocities, above 5 m/s.) The heat transfer

coefficient reaches approximately round 9 kW/m2K for the 100-micron channel at Re

= 3500 (6.5 m/s velocity) and decreases to below 4 kW/m2K for the 500-micron

channel. The relation between the heat transfer coefficient and Re is mathematically fit

to a power function (as shown in the Figure 53) where the heat transfer coefficient

varies as

!

Re0.57 ,

!

Re0.52 and

!

Re0.38 for the 100-, 200- and 500-micron channels,

respectively. This is in the range of expected exponents of literature correlations for

laminar developing flow and fully developed turbulent flow as the heat transfer

coefficient varies between

!

Re0.33 and

!

Re0.8 for laminar developing flow and turbulent

flow [25].

The single-phase hydraulic and thermal performance of the micro gap cooler, with

water as coolant, was also studied. Figures 54 and 55, show the water-based pressure

drop and heat transfer coefficient performance of micro gap channels as a function of

Re.

The thermal performance for water is much better than with HFE-7100, providing heat

transfer coefficients that are approximately three times larger than that of the HFE-

7100 values. The heat transfer coefficient performance with water reaches a value of

27 kW/m2K at 6.5 m/s velocity compared to 9kW/m

2K with HFE-7100 at the same

velocity. The relation between the heat transfer coefficient and Re is mathematically fit

to a power function (as shown in the Figure 55) where the heat transfer coefficient

varies as

!

Re0.49 ,

!

Re0.33 and

!

Re0.38 for the 100-, 200- and 500-micron channels,

100

respectively. This is in the range of expected exponents of literature correlations for

laminar developing flow and turbulent flow as the heat transfer coefficient varies

between

!

Re0.33 and

!

Re0.8 for laminar developing flow and turbulent flow [25].


Heights, flowing HFE-7100, Tin=23°C, q!=7W/cm2.

101


Channel Heights, flowing HFE-7100, Tin=23°C, q!=7W/cm2.

102


Heights, flowing Water, Tin=23°C, q!=7W/cm2.


Channel Heights, flowing Water, Tin=23°C, q!=7W/cm2.

6.5 Conclusions

The chapter discusses in detail the various aspects of single-phase heat transfer for a

chip-scale micro gap channel cooler. Overall pressure drop and heat transfer

coefficient were studied for the various channels considered and with HFE-7100, as

well as water, as the working fluids. The pressure drop was found to be inversely

proportional to the channel height for a fixed Re number (fixed flow rate.) For HFE-

103

7100, the pressure drop, for a fixed velocity of 6.5 m/s, increases from around 20,000

Pa for the 500-micron channel to 80,000 Pa for the 100-micron channel. The heat

transfer coefficient is also inversely proportional to the channel height for a fixed Re

number (fixed velocity.) The heat transfer coefficient function is pseudo linear as a

function of Re number spanning the range from laminar to turbulent at high flow rates

(above 5 m/s.) For HFE-7100, the heat transfer coefficient reaches around 9 kW/m2K

for the 100-micron channel at around Re = 3500 (6.5 m/s velocity.) This heat transfer

coefficient decreases to below 4 kW/m2K for the 500-micron channel.

The single phase pressure drop performance of micro gap channels, with water, is

similar to that of HFE-7100 across all Re. The thermal performance for water,

however, is much better than with HFE-7100. It is around three times larger than that

of HFE-7100. The heat transfer coefficient with water reaches a value of 27 kW/m2K

at 6.5 m/s velocity compared to 9 kW/m2K with HFE-7100 at the same velocity.

The literature correlations for pressure drop and heat transfer coefficient are well

suited for ideal channels with ideal boundary conditions, i.e., channel geometries with

the characteristics of uniform the flow, laminar-developing flow, uniform thermal

boundary conditions (flux or temperature) and neglected conjugate heat transfer effects.

The present work focused on a practical channel (non-ideal) with developing flow,

non-uniform heating, non-ideal geometry, and full conjugate heat transfer effects.

Although single-phase correlations captured the general dependence of the pressure

104

drop and the heat transfer coefficient on the flow rate in this microgap channel, they

have proven not to be accurate, especially at the low flow rate range. For HFE-7100

the average error of using the ideal channel pressure drop correlation is 24% and is

highest at the low velocity range (0.7-1.5 m/s.) Similarly, the average heat transfer

coefficient error is 7% and is highest at similar low velocity range (0.7-1.5 m/s.)

Numerical modeling using computational fluid dynamics software (CFD) was used in

order to overcome the inappropriateness of the available correlations. A CFD model

predicted well the conjugate heat transfer effects (the rate of heat dissipated by the

fluid as convective flow) versus the heat conducted through the chip substrate. It was

found, as predicted, that this conversion rate increases proportionally with the flow

rate and inversely with the channel height. Furthermore, CFD simulations correlated

well with experimental data with an error of 5% and much better than ideal channel-

based literature correlations (20% error) as the CFD model takes into account all the

geometric and boundary condition complexities not considered in the simple

correlations. CFD modeling not only predicted well the overall pressure and the heat

transfer coefficient for the various channels considered (5% error) but also predicted

well the junction plane temperature distribution. Another very important and rather

critical aspect that CFD modeling uncovered was the spatial distribution of heat flux at

the wall (die top surface) and resultant wall spatial the heat transfer coefficient.

Conduction spreading of the die silicon block (800-micron thick) played an important

role in changing the wall heat flux variations for all heating patterns considered

(uniform and non-uniform.) It was found that silicon conduction did obscure the

105

serpentine pattern on the wetted surface but always resulted in highly non-uniform

heat flux at the wall even when the heat was applied across the entire junction plane of

the chip. This provides a clear explanation for why available uniform heat flux

correlations failed to predict accurately the heat transfer coefficient. Knowing the wall

spatial variations of temperature and heat flux, CFD was used to inversely calculate

the spatial variations of wall the heat transfer coefficient. The spatial the heat transfer

coefficient was more non-uniform with non-uniform heating and was characterized by

the skewed symmetry toward the higher heat flux zones of the chip compared to

uniform heating. The flow field dominates the behavior of the heat transfer coefficient

and due to conduction spreading in the chip the differences in the thermal boundary

condition are minimized and have only a weak effect on the heat transfer coefficient

distribution.

106

Chapter 7:

Two-Phase Heat Transfer Experimental Data and Discussion

7.1 Introduction and basic relations

Two-phase heat transfer experiments of the 100, 200 and 500-micron channels, with

HFE-7100 coolant, with three different heating patterns (uniform, half die and

quadrant die heating,) were performed and analyzed under fully saturated conditions.

As noted in Chapter 3, the saturated two-phase experiments were performed on a

silicon thermal test chip resembling a commercially available microprocessor with a

total die surface area of 1.44 cm2. The thermal test chip was mounted in a hermetically

sealed chamber, with a predetermined channel height, i.e., 100-, 200- and 500- micron,

whereby cooling fluid HFE-7100 was pumped into it at a preset flow rate. An in-line

heater was used to heat up the fluid, incoming into the test channel, in order to achieve

the saturated condition immediately at the channel inlet. This saturated liquid

condition was determined by cross comparing the fluid inlet temperature against the

fluid inlet pressure, measured by the installed absolute pressure transducer, at the

channel inlet.

The thermal chip is 13.75 mm wide and 10.47 mm long (along the flow direction.)

This very short length is a key characteristic of this non-ideal channel as it causes the

fluid to be developing in the entire channel. The chip is heated by an embedded

107

serpentine heater at the junction plane of the silicon thermal chip. The embedded

heater enabled for various levels of heat fluxes at the thermal chip and various heating

patterns, i.e., uniform heating, half-die and quadrant-die non-uniform heating. A

detailed and overall description of the microgap channel two-phase apparatus is found

in Chapter 3.

The wall (die top surface) temperatures were captured by nine embedded temperature

diodes (sensors) spread at various locations at the thermal chip junction plane. The

heated (two-phase) fluid exiting the microgap channel is run through an externally

water-cooled flat plate heat exchanger to condense the two-phase mixture. The

condensate fluid is pumped through a centrifugal pump at a pre-determined flow rate

back into the channel through the in-line heater. A flow rate meter is installed at the

outlet of the pump to measure the fluid flow rate.

A set of saturated two-phase experiments were run through the 100, 200 and 500

micron channels, with variable mass flow rates and variable heat fluxes at the thermal

test chip.

The average wall temperature was calculated by averaging out the nine temperature

sensors embedded in the test chip. The heat conversion rate, i.e., the percentage of heat

going into the test channel as opposed to the heat conducted through the chip substrate

into the test board, is extracted from the output of the pseudo two-phase CFD model

based on the validated single-phase CFD model. The model, for each fixed flow rate,

heat flux and channel height, was run iteratively by altering the fluid properties until

108

the wall average temperature agreed with the experimental temperature data. The CFD

model can then provides the heat going into the channel versus the heat conducted into

the substrate, thus helping to resolve the conjugate heat transfer problem. The heat flux

is calculated by dividing the calculated “conversion rate” (i.e., heat flowing into the

channel) by the entire chip surface area (1.44 cm2). The two-phase exit quality of the

channel is calculated using the fully saturated channel energy equation as:

!

q' '"A = m•

"hfg " x (7.1)

Where

!

q' ' is the heat flux into the channel, A is the chip surface area,

!

m

•

is the mass

flow rate, hfg is the latent heat of vaporization and x is vapor exit quality. Due to the

very short microgap channel length, this calculated exit quality is used to characterize

the two-phase state of the test channel. The wall average two-phase channel heat

transfer coefficient is calculated by

)('' SatWallTP TThq != (7.2)

Where hTP is the wall average two-phase heat transfer coefficient, Twall is the wall

average temperature and Tsat is the channel average saturation temperature.

The uncertainty in the two-phase heat transfer coefficient, obtained from the channel

energy balance equation above, is linear and is affected by the uncertainties in the

109

measured quantities including the flow rate, the temperature of the wall (die sensors),

the temperature at the inlet, and the stability of the data logger and power supply. It

can be expressed mathematically as

!

"h

h

#

$ %

&

' (

2

="m

•

m•

#

$

% %

&

'

( (

2

+"q

q

#

$ %

&

' (

2

+")Twall)Twall

#

$ %

&

' (

2

(7.3)

Where

!

" h is uncertainty of heat transfer coefficient,

!

"m•

is the error of flow rate via

the flow meter,

!

"q is error of input power via the power supply,

!

"#Twall

is the

measurement error of wall super heat temperature. The flow meter’s flow rate error is

± 1.5%. The error of the power supply is ± 2.5%. The maximum error in the wall

super heat temperature measurement is ± 0.25°C which causes maximum error of 1%.

Thus, the possible maximum error of measuring the two-phase heat transfer coefficient

is ±3.1%.

The single-phase heat transfer experimental work detailed in Chapter 5, served to

validate the overall approach of measuring the channel heat transfer coefficient while

identifying the difficulty in applying classical correlations to actual chip cooling with

all the non-idealities we have encountered including flow-based, geometrical,

boundary conditions non-idealities.

110

The experimental data were reported as average heat transfer coefficient hTP versus

wall average heat flux,

!

q' ', and vapor quality, x, for the range of mass fluxes

considered. The mass flux (G), for each experiment, was calculated by dividing the

mass flow rate

!

m

•

by the channel cross-section area.

The range of mass flux considered was 350 kg/m2s to 1500 kg/m

2s reflecting an

overall flow rate range of 0.4-3 ml/s. The range of heat flux considered was 20-250

kW/m2. The area average heat transfer coefficient data for uniform heating is plotted

against the channel heat flux and the calculated vapor quality at the channel exit as

shown in Figures 56, 57 and 58, respectively.

Figure 56: Two-phase h vs. q! and x for Uniform Heated 100-micron Channel

Flowing HFE-7100.

111


Flowing HFE-7100.


Flowing HFE-7100.

7.2 Taitel-Dukler Flow Regime Map

Following Bar-Cohen and Rahim [20], classical Taitel-Dukler flow regime modeling

was performed on the 100-, 200- and 500-micron uniformly heated channels and the

112

locus of the two-phase mixture, as well as the heat transfer coefficient data, was

superimposed on the TD flow regime maps, as shown in Figures 59-61.

The map’s coordinates are the superficial gas velocity and superficial liquid velocity

given by

!

UG

S= x

G

"G

UL

S= (1# x)

G

"L

(7.4)

Where

!

UG

S is the superficial gas velocity and

!

UL

S is the superficial liquid velocity while

G (kg/m2s) is the mass flux, x is the exit quality and

!

"G

and

!

"L (kg/m

3) are the gas and

liquid density, respectively.

The TD map model determines the flow regime, i.e., Stratified, Bubbly, Intermittent or

Annular, for each binary set of superficial gas velocity and superficial liquid velocity

values.

The channel average heat transfer coefficient data calculated for various heat fluxes

are overlaid on the TD maps as a function of the superficial gas velocity (representing

the exit quality x) for a specific mass flux G.

113

The map has a characteristic angled transition line between the Annular and

Intermittent flow regimes (as shown in Figs 59-61). A modified Intermittent/Annuar

transition line was proposed by Rahim et al [57]. The modified line is a vertical one at

a fixed superficial gas velocity (as shown in Figs 59-61). The basis for the modified

vertical transition line will be discussed later.

Figure 59: Taitel-Dukler Map with Flow Regimes and h’s for Uniform Heating

and 100-micron Channel. G=350, 500, 650, 800, 1000 and 1500 kg/m2s.

114

Figure 60: Taitel-Dukler Map with Flow Regimes and h’s for Uniform heating

and 200-micron Channel. G=150, 350, 500, 650, 800, 1000 and 1500 kg/m2s.

115

Figure 61: Taitel-Dukler Map with Flow Regimes and h’s for Uniform Heating

and 500-micron Channel. G=80, 150, 270 and 350 kg/m2s.

Examining Fig 59, the flow regime map for the uniformly heated channel wall, it may

be seen that the two-phase loci for the mass fluxes examined in this study (350-1500

kg/m2s) traverse the superficial velocity plane at relatively high liquid velocities,

entering in (or close to) Bubble flow progressing through the Intermittent regime, and

terminating in the Annular regime. In this classical Taitel-Dukler map, the Intermittent

regime appears to dominate the behavior of the uniformly heated microgap channel for

the operating conditions studied. Similar observations can be made on the 200- and

500-micron channel flow regime maps shown in Figures 60 and 61, respectively. The

116

two-phase loci for these channels, with the mass fluxes studied (150-1500 kg/m2s for

the 200-micron channel and 80-350 kg/m2s for the 500-micron channel) experience

similar behavior to that of the 100-channel, however at lower overall superficial liquid

velocities such that the loci dos not start with Bubble but rather with Intermittent

regime (especially with the 500-micon channel) terminating at the Annular regime.

Although this mapping methodology has been used successfully for miniature

channels [20] and has helped to establish that Annular flow is the dominant flow

regime for two-phase flow in this form factor, it is to be noted that the present 100-

micron microgap channel, with the exception of the study by Kim et al [19], is

substantially smaller than, and operates at relatively higher mass fluxes, than nearly all

the data examined in the past. While the Tabatabai and Faghri flow regime map [44]

attempts to define a flow regime map for very small diameter tubes, Fig 62 reveals that

this map differs only in the boundary between Bubble and Intermittent flow and does

not alter the location of the Annular flow regime. It has also been suggested that the

Confinement Number, Co, defined as the ratio of the theoretical bubble departure

diameter to the tube diameter, could be used to identify true micro-channels [30]. For

Co > 0.5, individual vapor bubbles could be expected to fill the entire tube, leading to

Intermittent flow, and Co substantially larger than unity, as occurred in the present

work (Co = 4.5 for 100-micron channel and HFE-7100 coolant), would appear to

imply that Annular flow prevails in the channel.

117

Figure 62: Tabatabai & Faghri’s Modification to the Taitel-Dukler Map Showing

the Proposed Transition Line to Annular Flow [20].

Interestingly, Rahim et al [57] recently completed a detailed analysis of the flow

regimes encountered in the flow of refrigerants in sub-millimeter tubes. While the

T&D map was found to properly account for 2/3rds of the observations, use of

modified criteria for the transition from Intermittent to Annular flow, along with a

modification of the Bubble-to-Intermittent boundary, resulted in a correct

determination of the flow regime for more than 90% of the experimental data. A

modified Intermittent/Annular transition superficial gas velocity was proposed as

118

!

UG

S=6.2[" g(#L $ #G )]

1/ 4

#G1/ 2

(7.5)

This modified transition line, is also defined as a function of Weber number and Bond

number, as

!

We1/ 2

Bo1/ 4

= 6.2 (7.6)

Applying this modified transition superficial gas velocity to HFE-7100 yields a

transition value of

!

UG

S= 6.55 m/s. This modified vertical transition line, along with the

original diagonal transition line, were superimposed on Figs 59-61 for the TD maps for

the 100, 200 and 500-micron channels, respectively. The proposed vertical transition

line, superimposed on the 100- and 200-micron channels, leads to more data points

falling in the Annular regime at higher mass fluxes while it makes all the data points

fall in the Intermittent regime at the low mass fluxes. While on the 500-micron channel,

the proposed vertical transition line makes the entire data set fall in the intermittent

regime.

Taitel-Dukler flow regime modeling was also performed on the 100-, 200- and 500-

micron non-uniformly heated channels and the locus of the two-phase mixture, as well

as the heat transfer coefficient data, was superimposed on the TD flow regime maps.

The two types of non-uniformity studied are half-die and quadrant-die heating, and

119

their TD flow regime maps as shown in Figures 63-65 and Figures 66-68, for the two

heating types, respectively.

Examining the TD maps for the non-uniformly-heated channels in Figs 63-65, shows

that the two-phase loci for the mass fluxes examined in this study experience similar

trends to the uniformly heated channel, as they traverse the superficial velocity plane

at relatively high liquid velocities, entering in Bubble or Intermittent flow, depending

on the channel diameter, progressing through the Intermittent regime, and terminating

in the Annular regime, with the exception of higher mass fluxes (1000-1500 kg/m2s) as

they terminate at the Intermittent (or at boundary of Intermittent-Annular) regime.

Intermittent regime appears to dominate the behavior of the non-uniformly heated

channel (similarly to the uniformly-heated channel) for the operating conditions

studied.

120

Figure 63: Taitel-Dukler Map with Flow Regimes and h’s for Half-Die Heating


121



122


and 500-micron Channel. G=80, 150, 270 and 350 kg/m2s.

123

Figure 66: Taitel-Dukler Map with Flow Regimes and h’s for Quadrant-Die

Heating and 100-micron Channel. G=350, 500, 650, 800, 1000 and 1500 kg/m2s.

124


Heating and 200-micron Channel. G=150, 350, 500, 650, 800, 1000 and 1500

kg/m2s.

125


Heating and 500-micron Channel. G=80, 150, 270 and 350 kg/m2s.

7.3 Heat transfer characteristics

As previously indicated the figures containing the predicted flow regime maps for

uniformly heated 100 micron channel, i.e., Figs 59-61, also display the variation of the

surface-average heat transfer coefficient with the exit superficial velocities. Examining

Fig 59, it may be seen that for most of the mass fluxes studied the heat transfer

coefficients at low qualities (or superficial vapor velocity) display values close to 10

kW/m2K and then decrease steeply as the quality increases, bottoming at heat transfer

coefficient of 3-4 kW/m2K, then reversing and rising modestly or substantially

126

depending on the specific conditions. Some of the operating conditions display a

second maximum at higher qualities and then revert to lower h values.

The two-phase average heat transfer coefficients vs. exit quality, for the 100, 200- and

500-micron channels, shown in Figs 56-58 appear to display the key segments of the

M-shape characteristic curve reported in the literature for two-phase flow in miniature

channels [20].

Thus the data from Yang and Fujita [37] using R113 refrigerant and Diaz et al [38]

using n-Octane, presented by Bar-Cohen and Rahim [20] and displayed in Fig 69,

clearly show this behavior, with a decreasing trend in intermittent flow, a minimum

close to the transition to Annular flow, then a positive slope and a second peak for h in

the Annular regime, at higher qualities. While this characteristic behavior, including

the second peak is seen in the present data, for the 100-micron channel, the inflection

points do not correspond well to the regime transition shown in the classical T&D map.

Alternatively, when the recently proposed Intermittent/Annular transition criteria [57]

is applied to the present data, the heat transfer coefficient trough is seen to correspond

more closely to the onset of Annular and the up-sloping branch of the h curve is almost

entirely contained within the Annular regime.

The 100-micron channel data as well as the 200-micron and 500-micron channels are

plotted in Figures 70, 71 and 72, respectively, and show that heat transfer coefficient

127

curve, across the various ranges of mass flux, can be mathematically fitted with a

third-degree polynomial that is characterized by a minimum point right after the

transition to from intermittent to annular flow and a maximum point (peak) in annular

flow before dry-out starts taking place. It should be noted that the heat transfer

coefficient curves at low mass fluxes, for example, those of the 100-micron channel at

350-650 Kg/m2s do not show a distinctive minimum before the transition to Annular

regime and a distinctive peak at the Annular regime and could also be fitted by a

descending power function. However, examining Figs 71 and 72, for the 200-micorn

and 500-micron channels, respectively, it is seen that the third-degree polynomial is

the more general form of the heat transfer coefficient variation with quality.

Figure 69: Two-Phase h vs. Exit Quality x of the Yang&Fujita [37] and Diaz et al

[38] Data [20].

128


Microgap Channel.

129


Microgap Channel.

130


Microgap Channel.

It may be observed that, with the exception of the mass flux of 270 kg/m2s in the 500-

micron channel, for each channel diameter the higher the mass flux the higher the

achievable two-phase heat transfer coefficient. It should be noted that in two-phase

flow in the 100-micron channel, the peak heat transfer coefficient in the Annular flow

regime reaches ~ 7-.8 kW/m2K at G=1500 kg/m

2s and vapor quality of x=10%, while

only reaching h values around 2 kW/m2K at the low mass flux of G=350 kg/m

2s.

Using the third-degree polynomial equation relation, embedded in Figure 70, the peak

131

annular h value is extrapolated to reach 11.5 kW/m2K in the 200-micron channel at a

similar mass flux of G=1500 kg/m2s and at x=14%. In a 500-micron channel, h could

be expected to reach 9 kW/m2K at 270 kg/m

2s mass flux and 14% vapor quality,

according to the third-polynomial equation fit,

!

h = "1e7x3

+ 3e6x3"161663x + 7183.

7.4 Heat transfer characteristics with non-uniform heating

Two-phase heat transfer experiments of the 100, 200 and 500-micron channels, with

HFE-7100 coolant, with non-uniform heating patterns (half die and quadrant die

heating,) were performed and analyzed under fully saturated conditions. The range of

mass flux considered was 350 kg/m2s to 1500 kg/m

2s. The area average heat transfer

coefficient data (using the full area of the chip) for non-uniform heating is plotted

against the channel (average on the chip) heat flux and the calculated vapor quality at

the channel exit as shown in Figures 72-77.

Figure 73: Two-Phase h vs. q and x for Half-Die Heating and 100-micron

Channel.

132


Channel.


Channel.

133


Channel.


Channel.

134


Channel.

As with the uniform heating cases, the general trend with non-uniform heating is that

the higher the mass flux (G) the higher achievable two-phase heat transfer coefficient

(h) except with the 200 micron channel in which, G=650 kg/m2s delivers higher h than

G=800 kg/m2s.

It is important to note the spatially fluctuating heat transfer coefficient behavior in the

100-micron channel with half die non-uniformity heating, at the various power levels

applied as displayed in Fig. 72. This fluctuating behavior, i.e., h experiences more than

two peaks, could reflect errors in the inverse determination of the heat transfer

coefficients. Alternatively, these results could represent some inherent local instability

in the channel, and/or wave phenomena in the two-phase flow prevailing in the

channel, though – it should be noted that – no globally unstable flow conditions were

encountered in these experiments. The fluctuation in h appear to be suppressed at

135

higher channel heights and higher mass fluxes and can be seen only at low mass flux

levels with the 200 micron channel and completely vanishes with the 500-micron

channel.

Similar h values can be seen with the non-uniform half die heating cases as with the

uniform-heating cases. It should be noted that, with the 100-micron channel h reaches

an annular flow peak of ~7.5 kW/m2K at G=1500 kg/m

2s and vapor quality of x=7%,

while h levels around 2 kW/m2K at the low mass flux of G=350 kg/m

2s. The h value is

extrapolated to increase to around 10 kW/m2K with 200-micron channel at similar

mass flux level of 1500 kg/m2s and at around 8% vapor quality. The two-phase h,

however, goes down to around 2.2 kW/m2K at annular regime peak at G=350 kg/m

2s

and at x=8%. At 500-micron channel, h would reach 6 kW/m2K at 350 kg/m

2s mass

flux and 9% vapor quality level.

Quadrant-die non-uniformity heating shows no h fluctuation observed earlier with

half-die heating. Higher h levels, than those with uniform heating, are observed with

100-micron channel at the high mass flux level of 1500 kg/m2s where the annular flow

regime peak is estimated to be around 10 kW/m2K level and at 8% quality. Similar h

levels, to those with uniform heating, are observed with 200- and 500-micron channels

where h can reach an h value of 13 kW/m2K at 1500 kg/m

2s mass flux with the 200-

micron channel and an extrapolated value of 20 kW/m2K at the same mass flux with

the 500-micron channel.

136

Chapter 8:

Heat Transfer Correlations

8.1 Introduction

Chapter 6 provided a detailed calculation procedure of the two-phase heat transfer

coefficients for the various channel heights studied under the three different heating

patterns considered. The heat transfer coefficients obtained for the 100-, 200- and 500-

micron microgaps were compared to the predictions of the aforementioned Chen and

Shah correlations detailed in Chapter 4. Statistical analysis was performed to

determine the discrepancy between the values predicted by each of the correlations and

the channel heat transfer data. The relative discrepancy in the prediction of heat

transfer coefficients was calculated as:

!

"i =hmeasured

#hcorrelation

hmeasured

$100 (8.1)

And the average relative discrepancy for a set of data was calculated as:

!

"AVE ="i

ni=1

n

# (8.2)

137

A total number of 459 data points (experiments) were performed on all channels (100,

200 and 500-micron) and with three different heating types, i.e., uniform, half-die and

quadrant -die heating.

8.2 Dependence on Two-Phase Reynolds Number

As previously noted in Chapter 3, the dependence of the two-phase heat transfer

coefficient on the two-phase Reynolds Number underpins many of the classical and

commonly used two-phase heat transfer correlations. It is, therefore, of interest to

examine the variation of the two-phase heat transfer coefficient as a function of the

two-phase Reynolds number, defined in equation (3.16). The two-phase data of the

uniformly heated 100-, 200- and 500-micron microgap channels are plotted in Fig 79.

Figure 79 illustrates that the heat transfer coefficient versus two-phase Reynolds

number data are widely scattered, with no clear trend but an apparent tendency for a

stronger dependence at the lower Reynolds Numbers and a weaker dependence at the

higher values. The best fit found for the data is a power function h=68.3Retp0.68

with an

average error of 25.3% (equal to R2=0.67) and a maximum error of 106%.

138

Figure 79: Two-Phase Heat Transfer Coefficient versus Retp for All Uniformly

Heated Microgap Channels.

This less than satisfactory power law dependence on the two-phase Reynolds Number

is thought to reflect the inherent contribution of the distinct flow regimes encountered

in two-phase flow in the microgap channel. It is, thus, appropriate to look at the data

sorted by the different two-phase flow regimes as a way of improving the comparison

and correlation of the heat transfer coefficients. This approach is discussed in detail in

the subsequent sections.

8.3 Flow regime sorting based on TD transition line

The T&D flow regime maps for uniformly heated channels, shown in Chapter 7, are

used to sort the two-phase datasets into Annular and Intermittent flow regimes. Two

139

criteria for the transition line between Intermittent and Annular flow regimes were

implemented, namely, the classical T&D angled transition line and the modified

!

We1/ 2

Bo1/ 4

= 6.2 based superficial gas velocity vertical line [57]. The Chen correlation was

used to predict the heat transfer coefficients in the Annular flow regime while the Shah

correlation was used to predict those in the Intermittent flow regime. The errors (

!

"AVE ),

in percentages, associated with Chen and Shah correlations for both transition criteria,

in the uniformly heated channels, are shown in Table 11.

Table 11: Average error (

!

"AVE ) of Heat transfer Coefficient Predictions Sorted by

Annular and Intermittent Flow Regimes per Classical T&D Line and

!

We1/ 2

Bo1/ 4

= 6.2

Based Line-Uniformly-Heated Channel.

As it can be seen from the data in Table 11, the Chen correlation applied to Annular

flow shows better overall accuracy (41% with T&D and 31% with

!

We1/ 2

Bo1/ 4

= 6.2) than

the Shah correlation applied to Intermittent flow (86% with T&D and 93% with

!

We1/ 2

Bo1/ 4

= 6.2), using both transition line criteria. Using either transition line criteria, the

140

Shah correlation overall is not good in prediction of data in the Intermittent flow

regime. The

!

We1/ 2

Bo1/ 4

= 6.2 modified transition line criterion shows better accuracy than

the classical T&D transition line criteria in the Annular flow and. While the

!

We1/ 2

Bo1/ 4

= 6.2 modified transition line shows a very good overall accuracy of 31%, its

best accuracy is with the 200-micron channel in which the error is 11%.

Intermediate parameters used in the calculation of Chen heat transfer coefficients were

tabulated Table 12, for the 100 micron channels with two nominal mass fluxes

G=1000 kg/m2s and G=1500 kg/m

2s. The intermediate parameters include channel

hydraulic diameter Dh, heat flux q”, channel average quality x, mass flux G, Martinelli

parameter Xtt, convective boiling enhancement factor F, two-phase Reynolds number

Retp and pool boiling suppression factor S. The table also includes experimental

(testing) and the Chen based heat transfer coefficient and the error (

!

"i ) associated with

it.

141

Table 12: Parameters of Two-Phase Heat Transfer Chen Correlation on 100-

micron Channel, Showing Error Reduction by Setting Convective Enhancement

Term F=1.

Examining the intermediate parameters used in the calculations of Chen correlations,

listed in Table 12, it is important to note that the value of the nucleate boiling

suppression factor (S) across all cases studied was very close to 1 (this is actually true

for the entire 459 data sets used in the study.) Also, the two-phase Reynolds number

(Retp) experienced very low values across the data set (< 1700). In addition, the

142

average superficial gas velocity of the data points in Fig 59 is ~ 5m/s while the average

superficial liquid velocity is ~ 0.5 m/s. Therefore, for the expected void fractions in the

channel of more than 50%, relatively modest differences between the actual liquid and

vapor velocities might be encountered for the conditions studied in the channel,

suggesting that the convective enhancement in this study could be modest and that

setting F equal to unity may better capture the heat transfer rate in the studied

microgap channel. This was implemented and the values predicted by the Chen

correlation with F=1 were shown in the same table (Table 1) above.

8.4 Pseudo flow regime sorting based on the heat transfer coefficient characteristic

curve

While sorting the data based on the T&D flow regime maps, utilizing the two criteria

mentioned above for transition between Intermittent and Annular flows, did not show

very good overall accuracy, an attempt was made to sort the entire data based on the

characteristic features of the heat transfer coefficient vs. quality curve discussed in

details in Chapter 7. The sorted flow regimes, based on the characteristic h vs. x curve,

will be denoted “Pseudo Intermittent” and “Pseudo Annuar”.

The errors (

!

"AVE ) associated with pseudo Chen and pseudo Shah correlations were

tabulated in Tables 13-18, where Tables 13-14 are for uniform heating, Tables 15-16

are for half-die non-uniform heating while Tables 17-18 are for quadrant-die non-

uniform heating. As can be seen from the error tables, for each heating pattern, the

error data was categorized by channel height, i.e., 100, 200 or 500 micron, and was

143

further sorted by the pseudo flow regime based on the characteristic h curve discussed

earlier in Chapter 7, and illustrated in the example shown in Figure 80 below for the

uniformly heated 100 micron channel with mass flux G=1500 kg/m2s.

Figure 80: Characteristic Heat Transfer Coefficient Curve with Illustrated

Ranges of Pseudo Annular and Pseudo Intermittent Flow Regimes, Uniformly-

Heated 100-micron Channel, G =1500 kg/m2s.


!

"AVE ) of Heat Transfer Coefficient Predictions Using

Chen and Shah Correlations for Uniformly Heated Channels.

144


!



Characteristic Curve, for Uniformly Heated Channels.


!


Chen and Shah Correlations for Half-Die Heated Channels.

145


!



Characteristic Curve, for Half-Die Heated Channels.


!


Chen and Shah Correlations for Quadrant Heated Channels.

146


!



Characteristic Curve, for Quadrant Heated Channels.

Looking at the uniform heating category as a reference for comparing the Chen and

Shah correlations, as these correlations were established for uniform heat flux wall

pipes in the first place, it is clear the Chen and Shah correlations predict well data in

the pseudo Annular and pseudo Intermittent flow regimes, respectively. Chen’s overall

average error for predicting pseudo Annular flow regime data is 22% while that of

Shah for predicting pseudo Intermittent flow regime data is 38%. Chen’s best accuracy

is with the 200-micron channel (17%) followed by the 500-micron channel (23%) and

the 100-micron channel (30%). The accuracy of the Shah correlation prediction in the

intermittent regime improves with the increase of channel height, where it is of an

average error of 46% for the 100-micron channel, 35% for the 200-micron channel and

27% for the 500-micron channel.

Categorizing the data for the non-uniform heating patterns and showing the two

different types of non-uniformity considered in the study, along with the sorting by the

slope of the heat transfer coefficient curve, as shown in Tables 13 and 15, shows

similar results to the uniform heating, relative to the accuracy of the Shah predictions.

With the exception of the half-die heating pattern for which the error of the 200-

micron channel (40%) is higher than that of the 100-micron channel (30%) and the

500-micron channel experiences the best accuracy with 22% average error. On the

147

other hand, the Chen correlations show best accuracy with half-die heating (18%) as

compared to that of quadrant-die heating (32%).

The implementation of setting the Chen’s convective boiling enhancement term F

equal to is shown on the correlations accuracy Tables (13-18) for the entire data set.

The biggest effect of setting Chen with F=1 was on the uniformly heated 100 micron

channel, where the error decreases from 30% to 9%. This modification was not helpful

with the higher channels heights.

Looking at the non-uniformly heated channel data in Tables 16 and 18, it can be seen

that similar effect of setting F=1 can be obtained for the 100 micron channel as with

the uniformly heated channel, where the error is reduced from 22% to 14% in the half-

die heated channels and from 21% to 20% in the quadrant-die heated channels. For the

200- and 500-micron channels, this modification of F=1 has also a positive impact on

the overall accuracy error as it dropped by a few percentage points.

8.5 Inverse calculations of spatial heat transfer coefficient

In this section, the previously validated single-phase CFD model is used to inversely

determine the spatial distribution of the two-phase heat transfer coefficient.

Unfortunately, today’s CFD codes are incapable of directly modeling two-phase flow

and it is, thus, not possible to simulate ebullient heat transfer in a microgap channel.

Alternatively, it is possible to iteratively change the channel fluid properties, i.e.,

148

specific heat and thermal conductivity, until the model produces wall temperature

distributions, which closely match the values and the pattern of the experimental

results. The experimental and iteratively simulated temperature data are shown in

Table 19, for the three heating patterns in a 100 micron microgap channel, with 25W

heating and mass flux G=1500 Kg/m2s. The number of trials (using Icepack CFD code

[53]) needed for the iterative process was 4-5 per each case, while the final values for

the adjusted fluid properties, including specific heat and thermal conductivity, were ~

3.2 times higher than those of the single-phase (liquid-only) properties. While it was

very difficult to reach a good agreement, with all the sensor temperature data, on the

wall temperature distributions with the uniformly heated channel case, an attempt was

made to maintain the same wall average temperature as with the experimental results

(shown in Table 19.)

It is interesting to mention that a good agreement, with all the sensor temperature data,

was achieved with the non-uniformly heated channels both in temperature distributions

and wall average temperatures.

The conversion rate, i.e., the percentage of heat going into the channel and the spatial

wall heat flux were determined from the model by solving the conductive resistance on

cell-by-cell basis. Knowing the spatial wall heat flux and temperature distribution as

well as the pre-assigned fluid inlet temperature (saturated temperature from the

experimental cases,) the model was used to calculate and post process the wall heat

transfer coefficient on cell-by-cell basis, i.e., to obtain the spatial distribution of h.

149

This was done by implementing Newton’s second law of cooling on each cell of the

wall.

This spatial wall h, q! and temperature distribution determined by this process are

illustrated in Figures 81, 82 and 83, for the three heating patterns considered, namely,

uniform, half die and quadrant die heating, respectively. These cases represented the

tests with total power of 25W and mass flow rate of 1.6 ml/s (equivalent to G= 1500

Kg/m2s) on the 100-micron channel.

Table 19: Experimental (Two-Phase Test) and Iteratively Adjusted CFD Wall

Temperatures for Three Heating Patterns. 100 micron Channel, 25W, G= 1500

kg/m2s.

150


Channel and Uniform Heating. 25W, G= 1500 kg/m2s.

151


Channel and Half-Die Non-Uniform Heating. 25W, G= 1500 kg/m2s.

152


Channel and Quadrant-Die Non-Uniform Heating. 25W, G= 1500 kg/m2s.

8.6 Inverse calculations of local Chen-based heat transfer coefficient

It is helpful and insightful from a research as well as a design standpoint to know how

the Chen correlation would perform in predicting the local heat transfer coefficients

and not only the average wall h. In this section, a numerical process is implemented to

determine the efficacy of the Chen correlation in predicting the local wall h. The

channel cross-section is divided into a number of small axial tubes (sub-walls) and

each tube is further divided into a series of zones. It is assumed that the vapor quality

153

starts at zero at the beginning of all tubes (saturated conditions at channel inlet) and

increases linearly across the tube length to end at the experimentally predetermined

full exit quality at the channel outlet. Having determined the temperature, heat flux and

average quality for each of the zones earlier from CFD, the calculation is performed to

determine the Chen-based h for each of the zones.

These zonal Chen based h calculated values are compared to the zonal CFD based h.

The results are illustrated in Figures 84 and 85, for both uniform heating and non-

uniform heating cases. For the uniform heating case, it can be seen that the spatial

Chen h does not correlate well with the spatial CFD h zonal-wise. While CFD h

decreases axially along the channel axis, we see an opposite pattern, i.e., axial increase

with the Chen h along the channel axis. Chen however correlates well with CFD only

tube-wise if we consider h average values per each of the tubes. This is believed to be

due to the characteristics of geometrical and boundary conditions (non-uniform wall

heat flux) of the channel as being far from ideal channel conditions used in Chen

correlations. For the non-uniform heating case, it quite clear that the spatial Chen h do

not correlate with the spatial CFD h zonal-wise nor do they correlate tube-wise. This is

believed to be due to the same reasons mentioned above especially the highly non-

uniform wall heat flux in both axes of the wall, axially and cross-wise, respectively.

It is believed that the above technique of determination of local Chen based heat

transfer coefficient, can be successful with the implementation of a robust optimization

process for better correlation of local wall temperature distribution between the actual

154

two-phase test and the pseudo CFD model discussed in Section 8.4 above. A robust

optimization algorithm can be based on locally changing the fluid properties in the

pseudo CFD model in order to better correlate the local wall temperature distribution

with the actual two-phase tests.

Figure 84: Inversely Calculated Chen-based Spatial Heat Transfer Coefficient for

100-micron Channel and Uniform Heating. 25W, G= 1500 kg/m2s.

155

Figure 85: Inversely Calculated Chen-based Spatial Heat Transfer Coefficient for

100-micron Channel and Half-Die Non-Uniform Heating. 25W, G= 1500 kg/m2s.

8.7 Prediction of wall temperature distribution and hot spots of non-uniform heating

It is of great interest for the thermal designer to resolve, even approximately, the wall

temperature distribution and hot spot patterns associated with non-uniform heating or

die power maps. In this section, a simple semi-numerical approach is proposed for the

determination of wall temperature distribution, using correlation-derived heat transfer

coefficients on the wetted surface. Given its relative accuracy in predicting the average

heat transfer coefficients for the microgap channels, use can be made of the Chen

correlation for this procedure. The approach involves modeling the die and the

substrate in a detailed conduction model with the non-uniform heat source applied at

the die junction plane and a single, average value of the flow boiling heat transfer

coefficient applied to the wetted surface. In an alternative embodiment of this

156

approach, local values of the heat transfer coefficient could be imposed as the

boundary conditions.

The approach was implemented on the 25W, 1.6 ml/s (1500 kg/m2s) and 100-micron

channel with three different heating patterns, namely, uniform, half die and quadrant

die heating, respectively. Figure 86, shows the wetted wall (top die surface)

temperature distribution, for each of the three cases, of the CFD inversed representing

actual experiment (on the left) versus the CFD with prescribed average CFD inversed

heat transfer coefficient (on the right.) It is clear that this technique predicts well the

wall temperature pattern, including wall average temperature, locations of maximum

temperatures and the temperature rise of the hot spots. The tabulated data of average

and maximum wall temperature for these cases are listed in Table 20. The temperature

differences between the two approaches are very small (1-3°C). The table shows the

error associated with average wall temperatures to be 5.8%, 2.0% and 4.8% for

uniform, half-die and quadrant-de heating patterns, respectively. While the error

associated with maximum wall temperatures to be 5.9%, 5.4% and 2.3% for uniform,

half-die and quadrant-de heating patterns, respectively.

157

Figure 86: CFD Temperature Distribution vs. Conduction-Only Based Modeling

with Wall-Prescribed Average Chen-Based h. 25W, G= 1500 kg/m2s.

158

Table 20: Temperature Errors of Conduction-Only Model with Prescribed Chen-

Based Average h on Wall, 100-micron Channel Flowing HFE-7100, P=25W, G=

1500 kg/m2s.

8.8 Conclusions

Detailed analyses of two-phase heat transfer in non-ideal micro gap channels were

performed in Chapters 7 and 8. The data show that heat transfer coefficient in such

channels follows a similar M-shape characteristic curve, as a function of vapor quality,

to literature data. It was quite evident that the heat transfer coefficient curve, across the

various ranges of mass flux considered, can be mathematically fitted with a third-

159

degree polynomial that is characterized by a minimum point right after the transition

from intermittent to annular flow and a maximum point (peak) at annular flow.

The general trend of heat transfer coefficient is that the higher the mass flux (G) the

higher achievable two-phase heat transfer coefficient (h) with few exceptions.

Heat transfer coefficient, with the 100-micron channel h reaches an annular flow peak

of ~7.8 kW/m2K at G=1500 kg/m

2s and vapor quality of x=10%. The h value is

extrapolated to increase to around 12 kW/m2K with 200-micron channel at similar

mass flux level of 1500 kg/m2s and at around 15% vapor quality. At 500-micron

channel, h could be expected to reach 9 kW/m2K at 270 kg/m

2s mass flux and 14%

vapor quality level.

The peak two-phase HFE-7100 heat transfer coefficient values were nearly 3-4 times

as high as the single phase HFE-7100 values and sometimes exceed the cooling

capability associated with water under forced convection.

It is important to note the fluctuating behavior, with the 100-micron channel with half

die non-uniformity heating, of the heat transfer coefficient at the various power levels

applied. This fluctuating behavior, i.e., h experiences more than two peaks, could

reflect errors in the inverse determination of the heat transfer coefficients.

Alternatively, these results could represent some inherent local instability in the

channel, and/or wave phenomena in the two-phase flow prevailing in the channel,

though – it should be noted that – no globally unstable flow conditions were

160




channel. Similar thermal performance levels were reported for the non-uniform heating

cases as with the uniform heating ones however at slightly smaller vapor quality levels.

The Taitel-Dukler analytical flow regime map modeling suggests that majority of the

present data falls within the intermittent flow regime. However, it is believed that the

majority of data in this work fall into the annular flow regime. This belief is based on

modifications, by researchers to the T&D flow regime map and its transition line to

annular regime. The belief is also based on the very characteristic trend of heat

transfer coefficient going through the annular regime in the majority of the cases

considered.

While sorting the data based on the T&D flow regime maps, utilizing the original

T&D criterion and the modified

!

We1/ 2

Bo1/ 4

= 6.2 based superficial gas velocity criterion,

for transition between Intermittent and Annular flows, did not show very good overall

accuracy, an attempt was made to sort the entire data graphically based on the

characteristic features of the heat transfer coefficient curve. The sorted flow regimes,

based on the characteristic h vs. x curve, were denoted “Pseudo Intermittent” and

“Pseudo Annuar”.

161

Heat transfer coefficients correlated well with Shah correlations in the pseudo

intermittent flow regime and well with Chen correlations in the pseudo annular flow

regime. Chen’s overall average error for predicting the pseudo annular flow regime

data is 22% while that of Shah for predicting the pseudo intermittent flow regime data

is 38%. Chen’s best accuracy is with the 200-micron channel (17%) followed by the

500-micron channel (23%) and the 100-micron channel (30%). The accuracy of Shah

correlation prediction in the pseudo intermittent regime improves with the increase of

channel height, where it is of an average error of 46% for the 100-micron channel,

35% for the 200-micron channel and 27% for the 500-micron channel.

Categorizing the data per heating patterns and showing the two different types of non-

uniformity considered in the study, along with the flow regime sorting showed similar

correlations with the Shah errors with the exception with the half-die heating pattern

whereby the error of the 200-micron channel (40%) is higher than that of the 100-

micron channel (30%) and the 500-micron channel experiences the best accuracy with

22% average error. On the other hand, Chen correlations show best accuracy with half-

die heating (18%) as compared to that of quadrant-die heating (32%).


the value of the nucleate boiling suppression factor (S) across all cases studied was

very close to 1. In addition, the two-phase Reynolds number (Retp) experienced very

low values across the data set (< 1700) suggesting that the convective boiling

enhancement in this study could be modest and that setting F equal to unity may better

162

capture the heat transfer rate in the studied microgap channel. This was implemented

and the biggest effect of setting Chen with F=1 was on the uniformly heated 100

micron channel, where the error decreased from 30% to 9%. This modification was not

helpful with the higher channels heights.

Similar effect, by setting F=1, were obtained with the non-uniformly heated 100-

micron channel as with the uniformly heated channel, where the error is reduced from

22% to 14% in the half-die heated channels and from 21% to 20% in the quadrant-die

heated channels. For the 200- and 500-micron channels, this modification of F=1 had

also a positive impact on the overall accuracy error as it dropped by a few percentage

points.

Inverse calculations of the wall spatial heat transfer coefficient were successfully

demonstrated utilizing CFD. The spatial heat transfer coefficient was correlated with

their counterparts based on implementing Chen correlations. Although Chen provided

accurate predictions spatially with measurements for the uniform heating cases, they

however, did not correlate with the spatial measurements zonal-wise nor do they

correlate tube-wise. This is believed to be due to the highly non-uniform wall heat flux

in both axes of the wall, axially and cross-wise, respectively.

It is believed that the above technique of determination of local Chen based heat

transfer coefficient, can be successful with the implementation of a robust optimization

process for better correlation of local wall temperature distribution between the actual

two-phase test and the pseudo CFD model discussed in Section 8.4 above. A robust

163

optimization algorithm can be based on locally changing the fluid properties in the

pseudo CFD model in order to better correlate the local wall temperature distribution

with the actual two-phase tests.

Finally, a semi-numerical technique was introduced for the prediction of temperature

distribution and hot spots for non-uniform heating. The technique was based on

solving a conduction-only model and prescribing a fixed and uniform Chen based heat

transfer coefficient of the wall. The technique predicted well the wall temperature

pattern including locations for maximum and minimum temperatures including

locations and values of hot spots. The prediction error was largely due to the error

associated with Chen correlations predicting the average wall heat transfer coefficient.

164

Chapter 9:

Conclusions and Future Work

9.1 Conclusions

Microgap channel coolers flowing two-phase dielectric fluid have a good potential for

cooling advanced high power electronics for they provide good thermal performance

and eliminate the inherited TIM thermal resistance prevailing with indirect liquid

cooling techniques. They also can be considered as cost effective and reliable

technique compared to expensive microchannel-based coolers. In order, however, to

address the particular applications in the industry for such microgap channel coolers, a

detailed study of the two-phase performance characteristics under non-ideal conditions

including very short channel length, non-uniformly heated channels, conjugate heat

transfer effect and packaging in a chip-scale form factor. The present work focuses on

experimentally investigating and numerically modeling the two-phase as well as

single-phase characteristics of microgap channels under these practical non-ideal

boundary conditions for a “real world” thermal test chip.

Chapter 6 discussed in detail the various aspects of single-phase heat transfer for a

chip-scale micro gap channel cooler. Single-phase heat transfer and hydraulic

characterization is performed to establish the single-phase baseline performance of the

microgap channel and to validate the mesh-intensive CFD numerical model developed

for the test channel.

165

The pressure drop was found to be inversely proportional to the channel height for a

fixed Re number (fixed velocity.) For HFE-7100, the pressure drop, for a fixed

velocity of 6.5 m/s, increases from around 20,000 Pa for the 500-micron channel to

80,000 Pa for the 100-micron channel. The heat transfer coefficient is also inversely

proportional to the channel height for a fixed Re number (fixed velocity.) The heat

transfer coefficient function is pseudo linear as a function of Re number spanning the

range from laminar to transitional at high flow rates (above 5 m/s.). Convective heat

transfer coefficients for HFE-7100 flowing in a 100-micron microgap channel reached

9 kW/m2K at 6.5 m/s fluid velocity.

The thermal performance for water is much better than with HFE-7100. It is around

three times larger than that of HFE-7100. The heat transfer coefficient with water

reaches a value of 27 kW/m2K at 6.5 m/s velocity.

The literature correlations for pressure drop and heat transfer coefficient are well

suited for ideal channels with ideal boundary conditions, i.e., channel geometries with

the characteristics of uniform the flow, laminar-developing flow, uniform thermal

boundary conditions (flux or temperature) and neglected conjugate heat transfer effects.

The present work focused on a practical channel (non-ideal) with developing flow,

non-uniform heating, non-ideal geometry, and full conjugate heat transfer effects.

Although single-phase correlations captured the general dependence of the pressure

drop and the heat transfer coefficient on the flow rate in this microgap channel, they

have proven not to be accurate, especially at the low flow rate range. For HFE-7100

166

the average error of using the ideal channel pressure drop correlation is 24% and is

highest at the low velocity range (0.7-1.5 m/s.) Similarly, the average heat transfer

coefficient error is 7% and is highest at similar low velocity range (0.7-1.5 m/s.)

Numerical modeling using computational fluid dynamics software (CFD) was

extensively used in order to overcome the inappropriateness of the available

correlations. A mesh intensive CFD model was developed. Despite the highly non-

uniform boundary conditions imposed on the microgap channel, CFD model

simulation gave excellent agreement with the experimental data (to within 5%), while

the discrepancy with the predictions of the classical, “ideal” channel correlations in the

literature reached 20%.

Another very important and rather critical aspect that was uncovered by the CFD mode

was the spatial distribution of heat flux at the wall (die top surface) and resultant wall

spatial the heat transfer coefficient. Conduction spreading of the die silicon block

(800-micron thick) played an important role in changing the wall heat flux variations

for all heating patterns considered (uniform and non-uniform.) It was found that silicon

conduction did obscure the serpentine pattern on the wetted surface but always

resulted in highly non-uniform heat flux at the wall even when the heat was applied

across the entire junction plane of the chip. This provides a clear explanation for why

available uniform heat flux correlations failed to predict accurately the heat transfer

coefficient. Knowing the wall spatial variations of temperature and heat flux, CFD was

used successfully to inversely calculate the spatial variations of wall the heat transfer

167

coefficient. The spatial the heat transfer coefficient was more non-uniform with non-

uniform heating and was characterized by the skewed symmetry toward the higher

heat flux zones of the chip compared to uniform heating. The flow field dominates the

behavior of the heat transfer coefficient and due to conduction spreading in the chip

the differences in the thermal boundary condition are minimized and have only a weak

effect on the heat transfer coefficient distribution.

A detailed investigation of two-phase heat transfer in non-ideal micro gap channels,

with developing flow and significant non-uniformities in heat generation, was

performed in Chapters 7 and 8. Significant temperature non-uniformities were

observed with non-uniform heating, where the wall temperature gradient exceeded

30°C with a heat flux gradient of 3-30 W/cm2, for the quadrant-die heating pattern

compared to a 20°C gradient and 7-14 W/cm2 heat flux gradient for the uniform

heating pattern, at 25W heat and 1500 kg/m2s mass flux.

It is important to note the fluctuating behavior, with the 100-micron channel with half

die non-uniformity heating, of the heat transfer coefficient at the various power levels

applied. This fluctuating behavior, i.e., h experiences more than two peaks, could

reflect errors in the inverse determination of the heat transfer coefficients.

Alternatively, these results could represent some inherent local instability in the

channel, and/or wave phenomena in the two-phase flow prevailing in the channel,

though – it should be noted that – no globally unstable flow conditions were

168




channel. Similar thermal performance levels were reported for the non-uniform heating

cases as with the uniform heating ones however at slightly smaller vapor quality levels.

Taitel-Dukler analytical flow regime map modeling was developed and suggested that

majority of the present data falls within the intermittent flow regime. However, it is

believed that the majority of data in this work fall into the annular flow regime. This

belief is based on modifications, by researchers to the T&D flow regime map and its

transition line to annular regime. The belief is also based on the very characteristic

trend of heat transfer coefficient going through the annular regime in the majority of

the cases considered.

While sorting the data based on the T&D flow regime maps, utilizing the original

T&D criterion and the modified

!

We1/ 2

Bo1/ 4

= 6.2 based superficial gas velocity criterion,

for transition between Intermittent and Annular flows, did not show very good overall

accuracy, an attempt was made to sort the entire data graphically by flow regimes and

type of dependence on quality (variable slope of heat transfer coefficient characteristic

curve). The sorted flow regimes, based on the characteristic h vs. x curve, were

denoted “Pseudo Intermittent” and “Pseudo Annular”.

169

Heat transfer coefficients found to agree well with Shah correlations in the pseudo

intermittent flow regime (38%) and well with Chen correlations in the pseudo annular

flow regime (22%). Chen’s best accuracy is with the 200-micron channel (17%)

followed by the 500-micron channel (23%) and the 100-micron channel (30%). The

accuracy of Shah correlation prediction in the pseudo intermittent regime improves

with the increase of channel height, where it is of an average error of 46% for the 100-

micron channel, 35% for the 200-micron channel and 27% for the 500-micron channel.

Heat transfer coefficient, with the 100-micron channel was found to reach an annular

flow peak of ~8 kW/m2K at G=1500 kg/m

2s and vapor quality of x=10%. The heat

transfer coefficient is extrapolated to increase to around 12 kW/m2K with 200-micron

channel at similar mass flux level of 1500 kg/m2s and at around 15% vapor quality. At

500-micron channel, heat transfer coefficient reaches 9 kW/m2K at 270 kg/m

2s mass

flux and 14% vapor quality level.

The peak two-phase HFE-7100 heat transfer coefficient values were nearly 2.5-4 times

as high as the single phase HFE-7100 values and sometimes exceed the cooling

capability associated with water under forced convection.

Categorizing the data per heating patterns and showing the two different types of non-

uniformity considered in the study, along with the flow regime sorting showed similar

correlations with the Shah errors with the exception with the half-die heating pattern

whereby the error of the 200-micron channel (40%) is higher than that of the 100-

micron channel (30%) and the 500-micron channel experiences the best accuracy with

170

22% average error. On the other hand, Chen correlations show best accuracy with half-

die heating (18%) as compared to that of quadrant-die heating (32%).


the value of the nucleate boiling suppression factor (S) across all cases studied was

very close to 1. In addition, the two-phase Reynolds number (Retp) experienced very

low values across the data set (< 1700) suggesting that the convective boiling

enhancement in this study could be modest and that setting F equal to unity may better

capture the heat transfer rate in the studied microgap channel. This was implemented

and the biggest effect of setting Chen with F=1 was on the uniformly heated 100

micron channel, where the error decreased from 30% to 9%. This modification was not

helpful with the higher channels heights.

Similar effect, by setting F=1, were obtained with the non-uniformly heated 100-

micron channel as with the uniformly heated channel, where the error is reduced from

22% to 14% in the half-die heated channels and from 21% to 20% in the quadrant-die

heated channels. For the 200- and 500-micron channels, this modification of F=1 had

also a positive impact on the overall accuracy error as it dropped by a few percentage

points.

The use of inverse computation for determining two-phase heat transfer coefficients

was successfully developed and demonstrated. Further efforts are needed to provide

more precise local wall temperature agreement and enhance the technique accuracy. A

171

robust optimization algorithm can be based on locally changing the fluid properties in

the pseudo CFD model in order to better correlate the local wall temperature

distribution with the actual two-phase tests.

A semi-numerical first-order technique, using the Chen correlation, was found to yield

acceptable prediction accuracy (17%) for the wall temperature distribution and hot

spots in non-uniformly heated “real world” microgap channels cooled by two-phase

flow. The technique was based on solving a conduction-only model and prescribing a

fixed and uniform Chen based heat transfer coefficient of the wall. The technique

predicted well the wall temperature pattern including locations for maximum and

minimum temperatures including locations and values of hot spots. The prediction

error was largely due to the error associated with Chen correlations predicting the

average wall heat transfer coefficient.

9.2 Future work

In this dissertation a detailed modeling and characterization study of single-phase and

two-phase heat transfer was conducted on a chip-scale non-uniformly heated microgap

channel cooler. Thermal performance limits were established and comparisons with

literature correlations of heat transfer coefficient and analysis of two-phase flow

regimes were carried out. In order to complete the understanding of the thermofluid

characteristics of such microgap channels, a number of future investigations are

suggested as follows:

172

• The sorting the heat transfer coefficient data based on the T&D flow regime

maps, utilizing the original T&D criterion and the modified

!

We1/ 2

Bo1/ 4

= 6.2 based

superficial gas velocity criterion, for transition between Intermittent and

Annular flows, did not show very good overall accuracy. On the other hand,

the sorted flow regimes, based on the characteristic h vs. x curve, showed good

accuracy using the Shah correlation in the “Pseudo Intermittent” flow regime

and the Chen correlation in the “Pseudo Annular” flow regime. It is thus

suggested a revisit of this subject and an extended work on possibly modifying

the classical T&D transition lines for a predict better prediction of flow

regimes in true microgap channels.

• The non-uniform heating and conjugate heat transfer effects are becoming

critical characteristics of contemporary microprocessors and graphics chips

packages. It is therefore, suggested that a future work on analyzing two-phase

flow in microgap channels considers a wider range non-uniform heating

patterns and different heat transfer conjugate effects.

• It is helpful and insightful from a research as well as a design standpoint to

know how the Chen correlation would perform in predicting the local heat

transfer coefficients and not only the average wall h. The dissertation presented

a numerical process to determine the efficacy of the Chen correlation in

predicting the local wall heat transfer coefficients. It is believed that this

technique can be successful with the implementation of a robust optimization

173

process for better correlation of local wall temperature distribution between the

actual two-phase test and the pseudo CFD model. A suggested future work is

the investigation of a robust optimization algorithm that can be based on

locally changing the fluid properties in the pseudo CFD model in order to

better correlate the local wall temperature distribution with the actual two-

phase tests.

• This dissertation established two-phase heat transfer performance ranges for a

chip-scale microgap channel housing an actual bare die thermal test chip and

flowing HFE-7100. An extension of this study, is suggested, to utilize other

fluids including water/glycol mixtures and lower boiling point Novec fluids

such as HFE-7000 and develop a two-phase thermal performance envelope as a

function of thermo-physical properties of utilized fluids.

174

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CHARACTERIZATION AND MODELING OF TWO-PHASE HEAT

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